diff --git a/paper/benchmark/Project.toml b/paper/benchmark/Project.toml
index 1ce22a2..8f5a652 100644
--- a/paper/benchmark/Project.toml
+++ b/paper/benchmark/Project.toml
@@ -1,8 +1,12 @@
 [deps]
 CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
 Carlo = "780c37f4-4e5a-43de-9e79-65c261e525a4"
+HDF5 = "f67ccb44-e63f-5c2f-98bd-6dc0ccc4ba2f"
 Ising = "a4b17d44-13d4-4c91-98cd-0449bec393fd"
 JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
 LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
+MakieCore = "20f20a25-4f0e-4fdf-b5d1-57303727442b"
+Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
+StochasticSeriesExpansion = "1c8cc5bc-bd94-4f4b-9471-62b736d0cc39"
diff --git a/paper/benchmark/benchmark_plots.jl b/paper/benchmark/benchmark_plots.jl
index e371155..24c8f23 100644
--- a/paper/benchmark/benchmark_plots.jl
+++ b/paper/benchmark/benchmark_plots.jl
@@ -1,4 +1,5 @@
 using CairoMakie
+using MakieCore
 using DelimitedFiles
 using DataFrames
 using LaTeXStrings
@@ -10,25 +11,31 @@ using Printf
 import Plots
 import Measurements: value, uncertainty
 
-default_theme() = Theme(
-    Axis = (xtickalign = 1, ytickalign = 1, xgridvisible = false, ygridvisible = false),
-)
-
-function plot_example()
-    df = DataFrame(ResultTools.dataframe("data/example_job.results.json"))
+include("makie.jl")
 
+function plots_defaults()
     Plots.default(
         linewidth = 2,
         framestyle = :box,
-        size = (350, 300),
+        size = (390, 280),
         label = nothing,
         grid = false,
         markerstrokecolor = :black,
         thickness_scaling = 1,
         tickfontsize = 8,
+        lw = 2,
         legendfontsize = 8,
         legendtitlefontsize = 10,
+        labelfontsize = 8,
+        palette = Plots.palette(Makie.wong_colors()),
     )
+end
+
+
+function plot_example()
+    df = DataFrame(ResultTools.dataframe("data/example_job.results.json"))
+
+    plots_defaults()
     Plots.plot(
         df.T,
         df.BinderRatio;
@@ -44,7 +51,7 @@ function plot_scaling()
     data = readdlm("data/benchmark.dat", ',')
 
     set_theme!(default_theme())
-    fig = Figure(size = (300, 250))
+    fig = Figure(size = (390, 280))
     ax = Axis(
         fig[1, 1],
         xscale = log10,
@@ -56,7 +63,7 @@ function plot_scaling()
 
     scatter!(ax, data[:, 1], data[:, 2])
     lines!(ax, data[:, 1], data[end, 2] * data[end, 1] ./ data[:, 1])
-    save("../figs/scaling.pdf", fig)
+    save("../figs/scaling.pdf", fig, pt_per_unit = 0.625)
     fig
 end
 
@@ -65,7 +72,7 @@ function plot_stats()
     data = DataFrame(ResultTools.dataframe("data/error_bench.results.json"))
 
 
-    fig = Figure(size = (500, 250))
+    fig = Figure(size = (600, 280))
 
     ax1 = Axis(fig[1, 1], xlabel = "Energy per spin", ylabel = "Probability density")
     ax2 = Axis(fig[1, 2], xlabel = "Binder ratio")
@@ -117,7 +124,7 @@ function plot_stats()
 
     # text!(ax2, 0.5, 0.75, space=:relative, align=(:center, :center), justification=:center, text = "T = 2.3\nL = 20")
 
-    save("../figs/stats.pdf", fig)
+    save("../figs/stats.pdf", fig, pt_per_unit = 0.625)
     fig
 end
 
@@ -182,3 +189,111 @@ function plot_autocorr!(ax, path, obsname)
 
     xlims!(ax, -30, 300)
 end
+
+function plot_language_comparison()
+    set_theme!(default_theme())
+    julia_data = DataFrame(ResultTools.dataframe("data/ffb.results.json"))
+    cpp_data = DataFrame(ResultTools.dataframe("data/ffb_frust.results.json"))
+
+    fig = Figure(size = (390, 280))
+    ax = Axis(
+        fig[1, 1],
+        xlabel = L"Inverse temperature $\fontfamily{TeXGyreHeros}J/T$",
+        ylabel = "Time per sweep (ms)",
+    )
+
+    colors = Makie.wong_colors()[1:2]
+
+    plot!(
+        ax,
+        1 ./ cpp_data.T,
+        color = colors[2],
+        marker = :rect,
+        value.(1000 * cpp_data._ll_sweep_time),
+        label = "sweep (C++)",
+    )
+    plot!(
+        ax,
+        1 ./ julia_data.T,
+        color = colors[1],
+        marker = :circle,
+        value.(1000 * julia_data._ll_sweep_time),
+        label = "sweep (Julia)",
+    )
+    plot!(
+        ax,
+        1 ./ cpp_data.T,
+        strokewidth = 1,
+        strokecolor = colors[2],
+        color = :white,
+        marker = :rect,
+        value.(1000 * cpp_data._ll_measurement_time),
+        label = "measure (C++)",
+    )
+    plot!(
+        ax,
+        1 ./ julia_data.T,
+        strokewidth = 1,
+        strokecolor = colors[1],
+        color = :white,
+        marker = :circle,
+        value.(1000 * julia_data._ll_measure_time),
+        label = "measure (Julia)",
+    )
+    ylims!(ax, -0.4, 10.99)
+
+    axislegend(ax, position = :lt)
+    save("../figs/language_comparison.pdf", fig, pt_per_unit = 0.625)
+    return fig
+end
+
+function plot_banivo()
+    df = DataFrame(ResultTools.dataframe("data/bani2v2o8.results.json"))
+
+    df.L = [lattice["size"][1] for lattice in df.lattice]
+    plots_defaults()
+
+    p = Plots.plot(
+        df.T,
+        df.MagChi,
+        group = df.L,
+        xlabel = L"Temperature $T/J$",
+        ylabel = L"Magnetic susceptibility $χ^z J$",
+        legend_title = "L",
+    )
+
+    Plots.savefig("../figs/bani2v2o8.pdf")
+end
+
+function plot_parallel_tempering()
+    df2 = filter(
+        :Lx => ==(64),
+        DataFrame(ResultTools.dataframe("data/parallel_tempering_comparison.results.json")),
+    )
+    df = filter(
+        :Lx => ==(64),
+        DataFrame(ResultTools.dataframe("data/parallel_tempering.results.json")),
+    )
+
+
+    set_theme!(default_theme())
+    fig = Figure(size = (390, 280))
+    ax = Axis(
+        fig[1, 1],
+        ylabel = L"\fontfamily{TeXGyreHeros}Specific Heat $C$",
+        xlabel = L"Temperature $\fontfamily{TeXGyreHeros}T/J$",
+    )
+
+    Ts = df.parallel_tempering[1]["values"]
+
+    measplot!(ax, df2.T, df2.SpecificHeat, label = "no parallel tempering")
+
+    for (L, SpecificHeat) in zip(df.Lx, df.SpecificHeat)
+        measplot!(ax, Ts, SpecificHeat, label = "parallel tempering", marker = :rect)
+    end
+
+    axislegend(ax)
+
+    save("../figs/parallel_tempering.pdf", fig, pt_per_unit = 0.625)
+
+end
diff --git a/paper/benchmark/data/bani2v2o8.results.json b/paper/benchmark/data/bani2v2o8.results.json
new file mode 100644
index 0000000..55de0aa
--- /dev/null
+++ b/paper/benchmark/data/bani2v2o8.results.json
@@ -0,0 +1,11402 @@
+[
+ {
+  "task": "/mnt/home/lweber/src/StochasticSeriesExpansion/examples/bani2v2o8.data/task0001",
+  "parameters": {
+   "J": 1,
+   "S": 1,
+   "T": 0.05,
+   "lattice": {
+    "size": [
+     10,
+     10
+    ],
+    "unitcell": {
+     "bonds": [
+      {
+       "jd": [
+        0,
+        0
+       ],
+       "juc": 2,
+       "iuc": 1
+      },
+      {
+       "jd": [
+        0,
+        1
+       ],
+       "juc": 1,
+       "iuc": 2
+      },
+      {
+       "jd": [
+        1,
+        0
+       ],
+       "juc": 1,
+       "iuc": 2
+      }
+     ],
+     "sites": [
+      {
+       "coordination": 3,
+       "pos": [
+        0.0,
+        0.0
+       ],
+       "sublattice_sign": 1
+      },
+      {
+       "coordination": 3,
+       "pos": [
+        0.3333333333333333,
+        0.3333333333333333
+       ],
+       "sublattice_sign": -1
+      }
+     ],
+     "lattice_vectors": [
+      [
+       0.8660254037844386,
+       -0.5
+      ],
+      [
+       1.224744871391589,
+       0.5
+      ]
+     ]
+    }
+   },
+   "Dz": 0.005645,
+   "sweeps": 80000,
+   "measure": [
+    "magnetization"
+   ],
+   "model": "MagnetModel",
+   "thermalization": 10000,
+   "binsize": 100
+  },
+  "results": {
+   "SignMag2": {
+    "error": 1.8986269015267374e-7,
+    "autocorr_time": 0.33703983991630837,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": 2.579211469534049e-5,
+    "rebin_count": 18
+   },
+   "SignEnergy": {
+    "error": 0.00019393811066941932,
+    "autocorr_time": 0.4493257793059655,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": -1.8273904480286827,
+    "rebin_count": 18
+   },
+   "_ll_sweep_time": {
+    "error": 3.695436694516191e-5,
+    "autocorr_time": 10.04007554298059,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": 0.0021997342985663085,
+    "rebin_count": 18
+   },
+   "SignMagChi": {
+    "error": 0.0007594507606106966,
+    "autocorr_time": 0.3370398399163087,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": 0.10316845878136194,
+    "rebin_count": 18
+   },
+   "SignOperatorCount2": {
+    "error": 25382.39488726134,
+    "autocorr_time": 0.450909957507242,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": 2.6675489718724018e8,
+    "rebin_count": 18
+   },
+   "SignMag4": {
+    "error": 3.230208331467949e-11,
+    "autocorr_time": 0.3177165126269006,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": 2.0481630824372746e-9,
+    "rebin_count": 18
+   },
+   "MagChi": {
+    "error": [
+     0.0007594507606106957
+    ],
+    "autocorr_time": null,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": [
+     0.10316845878136216
+    ],
+    "rebin_count": 0
+   },
+   "OperatorCount": {
+    "error": 0.775752442677834,
+    "autocorr_time": 0.44932577923438766,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": 16332.141792114695,
+    "rebin_count": 18
+   },
+   "_ll_measure_time": {
+    "error": 1.578423568394996e-6,
+    "autocorr_time": 10.719065837212069,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": 0.0005554055450896057,
+    "rebin_count": 18
+   },
+   "Sign": {
+    "error": 0.0,
+    "autocorr_time": null,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": 1.0,
+    "rebin_count": 18
+   },
+   "Energy": {
+    "error": [
+     0.00019393811066962903
+    ],
+    "autocorr_time": null,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": [
+     -1.8273904480286802
+    ],
+    "rebin_count": 0
+   },
+   "BinderRatio": {
+    "error": [
+     0.002209795587017663
+    ],
+    "autocorr_time": null,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": [
+     0.3247647458594516
+    ],
+    "rebin_count": 0
+   },
+   "WormLengthFraction": {
+    "error": 0.05979347929387738,
+    "autocorr_time": 8.324773505828169,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": 2.2117585244524545,
+    "rebin_count": 18
+   },
+   "SignMag": {
+    "error": 4.604017807031167e-5,
+    "autocorr_time": 0.7521412109990617,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": 5.089605734767025e-5,
+    "rebin_count": 18
+   },
+   "Mag2": {
+    "error": [
+     1.8986269015267507e-7
+    ],
+    "autocorr_time": null,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": [
+     2.5792114695340478e-5
+    ],
+    "rebin_count": 0
+   },
+   "SignOperatorCount": {
+    "error": 0.775752442677834,
+    "autocorr_time": 0.44932577923438766,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": 16332.141792114695,
+    "rebin_count": 18
+   },
+   "Mag": {
+    "error": [
+     4.604017807031167e-5
+    ],
+    "autocorr_time": null,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": [
+     5.089605734767027e-5
+    ],
+    "rebin_count": 0
+   },
+   "AbsMag": {
+    "error": [
+     1.755454679754223e-5
+    ],
+    "autocorr_time": null,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": [
+     0.0036827956989247124
+    ],
+    "rebin_count": 0
+   },
+   "SpecificHeat": {
+    "error": [
+     0.5242652701346003
+    ],
+    "autocorr_time": null,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": [
+     -1.4493524952950558
+    ],
+    "rebin_count": 0
+   },
+   "SignAbsMag": {
+    "error": 1.755454679754196e-5,
+    "autocorr_time": 0.34017169878142944,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": 0.003682795698924734,
+    "rebin_count": 18
+   },
+   "Mag4": {
+    "error": [
+     3.230208331467945e-11
+    ],
+    "autocorr_time": null,
+    "rebin_len": 31,
+    "internal_bin_len": 100,
+    "mean": [
+     2.0481630824372717e-9
+    ],
+    "rebin_count": 0
+   }
+  },
+  "version": {
+   "carlo_version": "0.2.2",
+   "mc_package": "StochasticSeriesExpansion",
+   "mc_version": "0.1.0"
+  }
+ },
+ {
+  "task": "/mnt/home/lweber/src/StochasticSeriesExpansion/examples/bani2v2o8.data/task0002",
+  "parameters": {
+   "J": 1,
+   "S": 1,
+   "T": 0.2578947368421053,
+   "lattice": {
+    "size": [
+     10,
+     10
+    ],
+    "unitcell": {
+     "bonds": [
+      {
+       "jd": [
+        0,
+        0
+       ],
+       "juc": 2,
+       "iuc": 1
+      },
+      {
+       "jd": [
+        0,
+        1
+       ],
+       "juc": 1,
+       "iuc": 2
+      },
+      {
+       "jd": [
+        1,
+        0
+       ],
+       "juc": 1,
+       "iuc": 2
+      }
+     ],
+     "sites": [
+      {
+       "coordination": 3,
+       "pos": [
+        0.0,
+        0.0
+       ],
+       "sublattice_sign": 1
+      },
+      {
+       "coordination": 3,
+       "pos": [
+        0.3333333333333333,
+        0.3333333333333333
+       ],
+       "sublattice_sign": -1
+      }
+     ],
+     "lattice_vectors": [
+      [
+       0.8660254037844386,
+       -0.5
+      ],
+      [
+       1.224744871391589,
+       0.5
+      ]
+     ]
+    }
+   },
+   "Dz": 0.005645,
+   "sweeps": 80000,
+   "measure": [
+    "magnetization"
+   ],
+   "model": "MagnetModel",
+   "thermalization": 10000,
+   "binsize": 100
+  },
+  "results": {
+   "SignMag2": {
+    "error": 7.777089741302637e-7,
+    "autocorr_time": 0.43377885310670317,
+    "rebin_len": 42,
+    "internal_bin_len": 100,
+    "mean": 0.00012054730576441102,
+    "rebin_count": 19
+   },
+   "SignEnergy": {
+    "error": 0.0003086410933986468,
+    "autocorr_time": 0.35025709135883526,
+    "rebin_len": 42,
+    "internal_bin_len": 100,
+    "mean": -1.824971405817183,
+    "rebin_count": 19
+   },
+   "_ll_sweep_time": {
+    "error": 1.371376124384855e-6,
+    "autocorr_time": 1.188217460473004,
+    "rebin_len": 42,
+    "internal_bin_len": 100,
+    "mean": 0.00042172638516290725,
+    "rebin_count": 19
+   },
+   "SignMagChi": {
+    "error": 0.0006031212452438779,
+    "autocorr_time": 0.43377885310670544,
+    "rebin_len": 42,
+    "internal_bin_len": 100,
+    "mean": 0.09348566569484933,
+    "rebin_count": 19
+   },
+   "SignOperatorCount2": {
+    "error": 1512.1796544763774,
+    "autocorr_time": 0.3490510681197047,
+    "rebin_len": 42,
+    "internal_bin_len": 100,
+    "mean": 1.001759032933584e7,
+    "rebin_count": 19
+   },
+   "SignMag4": {
+    "error": 7.182382094737892e-10,
+    "autocorr_time": 0.41416294333240183,
+    "rebin_len": 42,
+    "internal_bin_len": 100,
+    "mean": 4.843473527568921e-8,
+    "rebin_count": 19
+   },
+   "MagChi": {
+    "error": [
+     0.0006031212452438754
+    ],
+    "autocorr_time": null,
+    "rebin_len": 42,
+    "internal_bin_len": 100,
+    "mean": [
+     0.09348566569484884
+    ],
+    "rebin_count": 0
+   },
+   "OperatorCount": {
+    "error": 0.23935431732956786,
+    "autocorr_time": 0.35025709137094996,
+    "rebin_len": 42,
+    "internal_bin_len": 100,
+    "mean": 3164.5596616541357,
+    "rebin_count": 19
+   },
+   "_ll_measure_time": {
+    "error": 4.995652500585736e-6,
+    "autocorr_time": 0.49259382078805036,
+    "rebin_len": 42,
+    "internal_bin_len": 100,
+    "mean": 0.00011719520010025062,
+    "rebin_count": 19
+   },
+   "Sign": {
+    "error": 0.0,
+    "autocorr_time": null,
+    "rebin_len": 42,
+    "internal_bin_len": 100,
+    "mean": 1.0,
+    "rebin_count": 19
+   },
+   "Energy": {
+    "error": [
+     0.0003086410933987977
+    ],
+    "autocorr_time": null,
+    "rebin_len": 42,
+    "internal_bin_len": 100,
+    "mean": [
+     -1.8249714058171804
+    ],
+    "rebin_count": 0
+   },
+   "BinderRatio": {
+    "error": [
+     0.002201837917636359
+    ],
+    "autocorr_time": null,
+    "rebin_len": 42,
+    "internal_bin_len": 100,
+    "mean": [
+     0.29999688582392636
+    ],
+    "rebin_count": 0
+   },
+   "WormLengthFraction": {
+    "error": 0.0067626463873282005,
+    "autocorr_time": 0.30612425098316887,
+    "rebin_len": 42,
+    "internal_bin_len": 100,
+    "mean": 2.2606773571851337,
+    "rebin_count": 19
+   },
+   "SignMag": {
+    "error": 5.314040091002143e-5,
+    "autocorr_time": 0.3533460335704864,
+    "rebin_len": 42,
+    "internal_bin_len": 100,
+    "mean": -5.733082706766914e-5,
+    "rebin_count": 19
+   },
+   "Mag2": {
+    "error": [
+     7.77708974130264e-7
+    ],
+    "autocorr_time": null,
+    "rebin_len": 42,
+    "internal_bin_len": 100,
+    "mean": [
+     0.00012054730576441068
+    ],
+    "rebin_count": 0
+   },
+   "SignOperatorCount": {
+    "error": 0.23935431732956786,
+    "autocorr_time": 0.35025709137094996,
+    "rebin_len": 42,
+    "internal_bin_len": 100,
+    "mean": 3164.5596616541357,
+    "rebin_count": 19
+   },
+   "Mag": {
+    "error": [
+     5.314040091002144e-5
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+    "mean": 551.8231578947368,
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+     0.00013152997350653542
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+    "rebin_len": 43,
+    "internal_bin_len": 100,
+    "mean": [
+     -9.68329253365971e-5
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+   "AbsMag": {
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+     4.729465415845505e-5
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+    "rebin_len": 43,
+    "internal_bin_len": 100,
+    "mean": [
+     0.018068222154222657
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+   },
+   "SpecificHeat": {
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+     0.005099861848591963
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+    "rebin_len": 43,
+    "internal_bin_len": 100,
+    "mean": [
+     0.11468123916684059
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+    "rebin_len": 43,
+    "internal_bin_len": 100,
+    "mean": 0.018068222154222758,
+    "rebin_count": 19
+   },
+   "Mag4": {
+    "error": [
+     8.147944305703708e-9
+    ],
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+    "rebin_len": 43,
+    "internal_bin_len": 100,
+    "mean": [
+     7.876082755304742e-7
+    ],
+    "rebin_count": 0
+   }
+  },
+  "version": {
+   "carlo_version": "0.2.2",
+   "mc_package": "StochasticSeriesExpansion",
+   "mc_version": "0.1.0"
+  }
+ }
+]
diff --git a/paper/benchmark/data/example_job.results.json b/paper/benchmark/data/example_job.results.json
index 9ea9f54..6391b61 100644
--- a/paper/benchmark/data/example_job.results.json
+++ b/paper/benchmark/data/example_job.results.json
@@ -1,6 +1,6 @@
 [
  {
-  "task": "example_job.data/task0001",
+  "task": "/mnt/home/lweber/src/Ising/example/example_job.data/task0001",
   "parameters": {
    "Ly": 8,
    "T": 1.0,
@@ -13,147 +13,167 @@
    "SpinCorrelation": {
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+    "error": 1.394528546700876e-8,
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+     8.840921420857964e-6
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    "Magnetization": {
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+    "error": 6.222899279013955e-5,
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     "rebin_len": 12,
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-    "mean": 0.9992773437500001,
+    "mean": -0.9992757161458333,
     "rebin_count": 16
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   },
   "version": {
-   "carlo_version": "0.2.0",
+   "carlo_version": "0.2.2",
    "mc_package": "Ising",
    "mc_version": "0.1.0"
   }
  },
  {
-  "task": "example_job.data/task0002",
+  "task": "/mnt/home/lweber/src/Ising/example/example_job.data/task0002",
   "parameters": {
    "Ly": 8,
-   "T": 1.2222222222222223,
+   "T": 1.1428571428571428,
    "Lx": 8,
    "sweeps": 20000,
    "thermalization": 2000,
@@ -163,147 +183,167 @@
    "SpinCorrelation": {
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+    "error": 1.5344214412123196e-9,
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-    "mean": 3.302413125e-6,
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    "Magnetization4": {
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   "version": {
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+   "carlo_version": "0.2.2",
    "mc_package": "Ising",
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   }
  },
  {
-  "task": "example_job.data/task0003",
+  "task": "/mnt/home/lweber/src/Ising/example/example_job.data/task0003",
   "parameters": {
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-   "T": 1.4444444444444444,
+   "T": 1.2857142857142858,
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    "sweeps": 20000,
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@@ -313,147 +353,167 @@
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diff --git a/paper/benchmark/data/ffb.results.json b/paper/benchmark/data/ffb.results.json
new file mode 100644
index 0000000..ebb0802
--- /dev/null
+++ b/paper/benchmark/data/ffb.results.json
@@ -0,0 +1,6434 @@
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diff --git a/paper/benchmark/data/ffb_frust.results.json b/paper/benchmark/data/ffb_frust.results.json
new file mode 100644
index 0000000..767f5a9
--- /dev/null
+++ b/paper/benchmark/data/ffb_frust.results.json
@@ -0,0 +1,4385 @@
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diff --git a/paper/benchmark/data/ffb_total_times.csv b/paper/benchmark/data/ffb_total_times.csv
new file mode 100644
index 0000000..71eee2d
--- /dev/null
+++ b/paper/benchmark/data/ffb_total_times.csv
@@ -0,0 +1,3 @@
+# language time(seconds)
+C++        1802
+Julia      608
diff --git a/paper/benchmark/data/parallel_tempering.results.json b/paper/benchmark/data/parallel_tempering.results.json
new file mode 100644
index 0000000..5d8bb80
--- /dev/null
+++ b/paper/benchmark/data/parallel_tempering.results.json
@@ -0,0 +1,9982 @@
+[
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diff --git a/paper/benchmark/data/parallel_tempering_comparison.results.json b/paper/benchmark/data/parallel_tempering_comparison.results.json
new file mode 100644
index 0000000..c144407
--- /dev/null
+++ b/paper/benchmark/data/parallel_tempering_comparison.results.json
@@ -0,0 +1,16442 @@
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+    "mean": 0.3630910464433523,
+    "rebin_count": 16
+   },
+   "Susceptibility": {
+    "error": [
+     0.0308317903264332
+    ],
+    "autocorr_time": null,
+    "rebin_len": 13,
+    "internal_bin_len": 100,
+    "mean": [
+     1.3554591778791796
+    ],
+    "rebin_count": 0
+   },
+   "SpecificHeat": {
+    "error": [
+     0.0024290090915739066
+    ],
+    "autocorr_time": null,
+    "rebin_len": 13,
+    "internal_bin_len": 100,
+    "mean": [
+     0.20023445756739155
+    ],
+    "rebin_count": 0
+   },
+   "Magnetization": {
+    "error": 0.0007683436175266021,
+    "autocorr_time": 0.6376191870522645,
+    "rebin_len": 13,
+    "internal_bin_len": 100,
+    "mean": -0.0008593984750600961,
+    "rebin_count": 16
+   }
+  },
+  "version": {
+   "carlo_version": "0.2.2",
+   "mc_package": "Ising",
+   "mc_version": "0.1.0"
+  }
+ }
+]
diff --git a/paper/benchmark/jobs/bani2v2o8.jl b/paper/benchmark/jobs/bani2v2o8.jl
new file mode 100644
index 0000000..7a7a321
--- /dev/null
+++ b/paper/benchmark/jobs/bani2v2o8.jl
@@ -0,0 +1,38 @@
+# bani2v2o8.jl
+
+using Carlo
+using Carlo.JobTools
+using StochasticSeriesExpansion
+
+tm = TaskMaker()
+tm.sweeps = 80000
+tm.thermalization = 10000
+tm.binsize = 100
+
+temperatures = range(0.05, 4, 20)
+system_sizes = [10, 20]
+
+tm.model = MagnetModel
+tm.S = 1
+tm.J = 1
+tm.Dz = 0.005645 # D^{QMC}_{EP(XY)}/J^{QMC}_n from PRB 104, 065502 
+
+tm.measure = [:magnetization]
+for L in system_sizes
+    tm.lattice = (unitcell = UnitCells.honeycomb, size = (L, L))
+
+    for T in temperatures
+        tm.T = T
+        task(tm)
+    end
+end
+
+job = JobInfo(
+    splitext(@__FILE__)[1],
+    StochasticSeriesExpansion.MC;
+    run_time = "24:00:00",
+    checkpoint_time = "30:00",
+    tasks = make_tasks(tm),
+)
+
+start(job, ARGS)
diff --git a/paper/benchmark/jobs/ffb.jl b/paper/benchmark/jobs/ffb.jl
new file mode 100755
index 0000000..4fa3b9b
--- /dev/null
+++ b/paper/benchmark/jobs/ffb.jl
@@ -0,0 +1,49 @@
+using Carlo
+using Carlo.JobTools
+using StochasticSeriesExpansion
+using Random
+
+tm = TaskMaker()
+tm.sweeps = 100000
+tm.thermalization = 10000
+tm.binsize = 100
+
+tm.model = ClusterModel
+tm.inner_model = MagnetModel
+tm.cluster_bases = (StochasticSeriesExpansion.ClusterBases.dimer,)
+
+tm.measure_quantum_numbers = [(; name = Symbol(), quantum_number = 2)]
+tm.parameter_map = (; J = vcat([:Jperp], repeat([:Jpar], 8)))
+
+tm.Jpar = 1
+tm.Jperp = 0.5
+
+βs = range(1, 10, 16)
+Ls = [30]
+
+for L in Ls
+    tm.lattice = (
+        unitcell = StochasticSeriesExpansion.UnitCells.fully_frust_square_bilayer,
+        size = (L, L),
+    )
+    for β in βs
+        tm.init_opstring_cutoff = 160000 * β / maximum(βs)
+        tm.init_num_worms = 8
+        tm.num_worms_attenuation_factor = 0.0
+        tm.T = 1 / β
+        tm.Lx = L
+        tm.Ly = L
+        task(tm)
+    end
+end
+
+job = JobInfo(
+    "~/ceph/carlo/ffb",
+    StochasticSeriesExpansion.MC;
+    run_time = "24:00:00",
+    checkpoint_time = "30:00",
+    rng = Random.MersenneTwister,
+    tasks = make_tasks(tm),
+)
+
+start(job, ARGS)
diff --git a/paper/benchmark/jobs/ffb_frust b/paper/benchmark/jobs/ffb_frust
new file mode 100755
index 0000000..62c5815
--- /dev/null
+++ b/paper/benchmark/jobs/ffb_frust
@@ -0,0 +1,33 @@
+#!/usr/bin/env python3
+
+# this is a job script for the C++ code StochasticSeriesExpansion.jl
+# is based on, available at https://github.com/lukas-weber/frust
+
+from loadleveller import taskmaker
+import numpy as np
+
+tm = taskmaker.TaskMaker(__file__, 'jobconfig.yml')
+tm.sweeps = 100000
+tm.thermalization = 10000
+tm.binsize = 100
+tm.lattice = 'bilayer'
+
+tm.measure = ['mag']
+
+tm.Jpar = 1
+tm.Jperp = 0.5
+
+βs = np.linspace(1,10,16)
+Ls = [30]
+
+for L in Ls:
+    for β in βs:
+        tm.init_opstring_cutoff = 160000*β/βs.max()
+        tm.init_num_worms = 8
+        tm.num_worms_attenuation_factor = 0.0
+        tm.T = 1/β
+        tm.Lx = L
+        tm.Ly = L
+        tm.task()
+
+tm.write()
diff --git a/paper/benchmark/jobs/jobconfig.yml b/paper/benchmark/jobs/jobconfig.yml
new file mode 100644
index 0000000..788d738
--- /dev/null
+++ b/paper/benchmark/jobs/jobconfig.yml
@@ -0,0 +1,19 @@
+num_cores: 16
+mem_per_cpu: 1G
+mpirun: srun --cpu-bind=cores
+
+
+custom_cmds: |
+  #SBATCH --partition=ccq
+  #SBATCH --mail-type=FAIL,END
+  #SBATCH -C 'ib-genoa'
+  #SBATCH --export=ALL
+  module purge
+  module load slurm gcc/13.2.0 openmpi4 python3 hdf5
+  source ~/venvs/qmc/bin/activate
+
+
+mc_walltime: '56:00:00'
+mc_runtime: '55:00:00'
+mc_checkpoint_time: '30:00'
+mc_binary: ~/src/frust/build/src/frust
diff --git a/paper/benchmark/jobs/parallel_tempering.jl b/paper/benchmark/jobs/parallel_tempering.jl
new file mode 100644
index 0000000..fe4e87d
--- /dev/null
+++ b/paper/benchmark/jobs/parallel_tempering.jl
@@ -0,0 +1,41 @@
+# parallel_tempering.jl
+
+using Carlo
+using Carlo.JobTools
+using Ising
+
+tm = TaskMaker()
+
+tm.sweeps = 20000
+tm.thermalization = 2000
+tm.binsize = 100
+
+Ts = range(1.5, 4, 30)
+
+# contract temperatures around Tc for better distribution overlap
+Tc = 2.269
+Ts += 0.5 .* (Tc .- Ts) ./ (0.6 .+ (Tc .- Ts) .^ 2)
+
+
+tm.parallel_tempering = (mc = Ising.MC, parameter = :T, values = Ts, interval = 1)
+
+Ls = [32, 64]
+for L in Ls
+    tm.Lx = L
+    tm.Ly = L
+
+    # tm.T is set implicitly by ParallelTemperingMC
+
+    task(tm)
+end
+
+job = JobInfo(
+    splitext(@__FILE__)[1],
+    ParallelTemperingMC; # the underlying model MC is set in tm.parallel_tempering.mc
+    run_time = "24:00:00",
+    checkpoint_time = "30:00",
+    tasks = make_tasks(tm),
+    ranks_per_run = length(tm.parallel_tempering.values), # needs to match!
+)
+
+start(job, ARGS)
diff --git a/paper/benchmark/jobs/parallel_tempering_comparison.jl b/paper/benchmark/jobs/parallel_tempering_comparison.jl
new file mode 100644
index 0000000..791e238
--- /dev/null
+++ b/paper/benchmark/jobs/parallel_tempering_comparison.jl
@@ -0,0 +1,36 @@
+# example_job.jl
+
+using Carlo
+using Carlo.JobTools
+using Ising
+
+tm = TaskMaker()
+
+tm.sweeps = 20000
+tm.thermalization = 2000
+tm.binsize = 100
+
+Ts = range(1.5, 4, 30)
+Tc = 2.269
+Ts += 0.5 .* (Tc .- Ts) ./ (0.6 .+ (Tc .- Ts) .^ 2)
+
+Ls = [4, 64]
+
+for L in Ls
+    for T in Ts
+        tm.T = T
+        tm.Lx = L
+        tm.Ly = L
+        task(tm)
+    end
+end
+
+job = JobInfo(
+    splitext(@__FILE__)[1],
+    Ising.MC;
+    run_time = "24:00:00",
+    checkpoint_time = "30:00",
+    tasks = make_tasks(tm),
+)
+
+start(job, ARGS)
diff --git a/paper/benchmark/makie.jl b/paper/benchmark/makie.jl
new file mode 100644
index 0000000..60910ec
--- /dev/null
+++ b/paper/benchmark/makie.jl
@@ -0,0 +1,45 @@
+using Measurements
+
+default_theme() = Theme(
+    figure_padding = 2,
+    Axis = (xtickalign = 1, ytickalign = 1, xgridvisible = false, ygridvisible = false),
+)
+
+
+@recipe MeasPlot (x, y) begin
+    errorcolor = @inherit markercolor
+    MakieCore.documented_attributes(Scatter)...
+end
+
+function Makie.plot!(mp::MeasPlot{<:Tuple{AbstractVector,AbstractVector}})
+    vals = @lift(Measurements.value.($(mp.y)))
+    errs = @lift(Measurements.uncertainty.($(mp.y)))
+    errorbars!(mp, mp.x, vals, errs, color = mp.errorcolor)
+    scatter!(
+        mp,
+        mp.x,
+        vals;
+        marker = mp.marker,
+        color = mp.color,
+        strokecolor = mp.strokecolor,
+        strokewidth = mp.strokewidth,
+    )
+    return mp
+end
+
+function Makie.legendelements(plot::MeasPlot, legend)
+    LegendElement[
+        LineElement(
+            linepoints = [Point2f(0.5, 0), Point2f(0.5, 1)],
+            color = plot.errorcolor,
+        ),
+        # MarkerElement(points = [Point2f(0.5, 0), Point2f(0.5, 1)], marker = :hline, markersize = 10),
+        MarkerElement(
+            points = [Point2f(0.5, 0.5)],
+            marker = plot.marker,
+            color = plot.color,
+            strokecolor = plot.strokecolor,
+            strokewidth = plot.strokewidth,
+        ),
+    ]
+end
diff --git a/paper/bibliography.bib b/paper/bibliography.bib
index 53b66d0..813f268 100644
--- a/paper/bibliography.bib
+++ b/paper/bibliography.bib
@@ -108,7 +108,7 @@ @article{BouchetValat2023
 	            a practical illustration of typical data processing operations.},
 	number = {4},
 	journal = {Journal of Statistical Software},
-	author = {Bouchet-Valat, Milan and Kamiński, Bogumił},
+	author = {Bouchet-Valat, Milan and Kaminski, Bogumil},
 	year = {2023},
 	pages = {1--32},
 }
@@ -184,3 +184,341 @@ @article{DanischKrumbiegel2021
 	         }},
 	journal = {Journal of Open Source Software},
 }
+
+@article{Torres2020,
+	title = {Emergent symmetries and coexisting orders in Dirac fermion systems},
+	author = {Torres, Emilio and Weber, Lukas and Janssen, Lukas and Wessel,
+	          Stefan and Scherer, Michael M.},
+	journal = {Phys. Rev. Res.},
+	volume = {2},
+	issue = {2},
+	pages = {022005},
+	numpages = {6},
+	year = {2020},
+	month = {Apr},
+	publisher = {American Physical Society},
+	doi = {10.1103/PhysRevResearch.2.022005},
+	url = {https://link.aps.org/doi/10.1103/PhysRevResearch.2.022005},
+}
+
+@article{Sandvik1999,
+	title = {Stochastic series expansion method with operator-loop update},
+	author = {Sandvik, Anders W.},
+	journal = {Phys. Rev. B},
+	volume = {59},
+	issue = {22},
+	pages = {R14157--R14160},
+	numpages = {0},
+	year = {1999},
+	month = {Jun},
+	publisher = {American Physical Society},
+	doi = {10.1103/PhysRevB.59.R14157},
+	url = {https://link.aps.org/doi/10.1103/PhysRevB.59.R14157},
+}
+
+@software{WeberStochasticSeriesExpansion2024,
+	author = {Weber, Lukas},
+	doi = {10.5281/zenodo.13993851},
+	month = oct,
+	title = {{StochasticSeriesExpansion.jl}},
+	year = {2024},
+}
+
+@software{WeberFrust2024,
+	author = {Weber, Lukas},
+	doi = {10.5281/zenodo.14205557},
+	month = nov,
+	title = {{frust}},
+	year = {2024},
+}
+
+@article{Jimenez2021,
+	title = {A quantum magnetic analogue to the critical point of water},
+	volume = {592},
+	ISSN = {1476-4687},
+	url = {http://dx.doi.org/10.1038/s41586-021-03411-8},
+	DOI = {10.1038/s41586-021-03411-8},
+	number = {7854},
+	journal = {Nature},
+	publisher = {Springer Science and Business Media LLC},
+	author = {Jiménez, J. Larrea and Crone, S. P. G. and Fogh, E. and Zayed, M.
+	          E. and Lortz, R. and Pomjakushina, E. and Conder, K. and Läuchli,
+	          A. M. and Weber, L. and Wessel, S. and Honecker, A. and Normand, B.
+	          and Rüegg, Ch. and Corboz, P. and Rønnow, H. M. and Mila, F.},
+	year = {2021},
+	month = apr,
+	pages = {370–375},
+}
+
+@article{Weber2022,
+	title = {{Quantum Monte Carlo simulations in the trimer basis: first-order
+	         transitions and thermal critical points in frustrated trilayer
+	         magnets}},
+	author = {Lukas Weber and Andreas Honecker and Bruce Normand and Philippe
+	          Corboz and Frédéric Mila and Stefan Wessel},
+	journal = {SciPost Phys.},
+	volume = {12},
+	pages = {054},
+	year = {2022},
+	publisher = {SciPost},
+	doi = {10.21468/SciPostPhys.12.2.054},
+	url = {https://scipost.org/10.21468/SciPostPhys.12.2.054},
+}
+
+@incollection{Pan2024,
+	title = {The sign problem in quantum Monte Carlo simulations},
+	editor = {Tapash Chakraborty},
+	booktitle = {Encyclopedia of Condensed Matter Physics (Second Edition)},
+	publisher = {Academic Press},
+	edition = {Second Edition},
+	address = {Oxford},
+	pages = {879-893},
+	year = {2024},
+	isbn = {978-0-323-91408-6},
+	doi = {https://doi.org/10.1016/B978-0-323-90800-9.00095-0},
+	url = {
+	       https://www.sciencedirect.com/science/article/pii/B9780323908009000950
+	       },
+	author = {Gaopei Pan and Zi Yang Meng},
+	keywords = {Quantum Monte Carlo, Sign problem, Strongly correlated electrons
+	            },
+	abstract = {The sign problem in quantum Monte Carlo (QMC) simulations
+	            appears to be an extremely hard yet interesting problem. In this
+	            article, we present a pedagogical overview of the origin of the
+	            sign problem in various quantum Monte Carlo simulation techniques
+	            , ranging from the world-line and stochastic series expansion
+	            Monte Carlo for boson and spin systems to the determinant and
+	            momentum-space quantum Monte Carlo for interacting fermions. We
+	            point out the basis dependency of the sign problem and summarize
+	            the progresses to cure, ease and even make use of the sign
+	            problem over the years, such as symmetry analysis of the
+	            underlying Hamiltonian, basis optimization in writing down the
+	            partition functions and many others. Moreover, we state that
+	            although traditional lore says that in the case of sign problem,
+	            the average sign in QMC simulation approaches zero exponentially
+	            fast with the space-time volume of the configurational space,
+	            there are recent breakthroughs showing this is not always the
+	            case. Based on the properties of the partition function for
+	            finite size systems, one could distinguish when the average sign
+	            has the usual exponential scaling and when it is bestowed with an
+	            algebraic scaling at the low-temperature limit. Fermionic QMC
+	            simulations with such algebraic sign problems have been
+	            successfully carried out for extended Hubbard-type and quantum
+	            Moiré lattice models.},
+}
+
+
+@article{WeberCluster2022,
+	title = {Cluster quantum Monte Carlo study of two-dimensional weakly coupled
+	         frustrated trimer antiferromagnets},
+	author = {Weber, Lukas and Caci, Nils and Wessel, Stefan},
+	journal = {Phys. Rev. B},
+	volume = {106},
+	issue = {3},
+	pages = {035141},
+	numpages = {10},
+	year = {2022},
+	month = {Jul},
+	publisher = {American Physical Society},
+	doi = {10.1103/PhysRevB.106.035141},
+	url = {https://link.aps.org/doi/10.1103/PhysRevB.106.035141},
+}
+
+@article{WeberThermal2022,
+	title = {Thermal critical points from competing singlet formations in fully
+	         frustrated bilayer antiferromagnets},
+	author = {Weber, Lukas and Fache, Antoine Yves Dimitri and Mila, Fr\'ed\'
+	          eric and Wessel, Stefan},
+	journal = {Phys. Rev. B},
+	volume = {106},
+	issue = {23},
+	pages = {235128},
+	numpages = {7},
+	year = {2022},
+	month = {Dec},
+	publisher = {American Physical Society},
+	doi = {10.1103/PhysRevB.106.235128},
+	url = {https://link.aps.org/doi/10.1103/PhysRevB.106.235128},
+}
+
+@article{weber_cavityrenormalized_2023,
+	title = {Cavity-{{Renormalized Quantum Criticality}} in a {{Honeycomb
+	         Bilayer Antiferromagnet}}},
+	author = {Weber, Lukas and Vi{\~n}as Bostr{\"o}m, Emil and Claassen, Martin
+	          and Rubio, Angel and Kennes, Dante M.},
+	year = {2023},
+	month = sep,
+	journal = {Commun Phys},
+	volume = {6},
+	number = {1},
+	pages = {1--11},
+	publisher = {Nature Publishing Group},
+	issn = {2399-3650},
+	doi = {10.1038/s42005-023-01359-x},
+	copyright = {2023 The Author(s)},
+	keywords = {Phase transitions and critical phenomena,Polaritons},
+}
+
+@article{MullerHartmannExact2000,
+	title = {Exact Demonstration of Magnetization Plateaus and First-Order
+	         Dimer-N\'eel Phase Transitions in a Modified Shastry-Sutherland
+	         Model for ${\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}$},
+	author = {M\"uller-Hartmann, Erwin and Singh, Rajiv R. P. and Knetter,
+	          Christian and Uhrig, G\"otz S.},
+	journal = {Phys. Rev. Lett.},
+	volume = {84},
+	issue = {8},
+	pages = {1808--1811},
+	numpages = {0},
+	year = {2000},
+	month = {Feb},
+	publisher = {American Physical Society},
+	doi = {10.1103/PhysRevLett.84.1808},
+	url = {https://link.aps.org/doi/10.1103/PhysRevLett.84.1808},
+}
+
+@article{Alet2016,
+	title = {Sign-Problem-Free Monte Carlo Simulation of Certain Frustrated
+	         Quantum Magnets},
+	author = {Alet, Fabien and Damle, Kedar and Pujari, Sumiran},
+	journal = {Phys. Rev. Lett.},
+	volume = {117},
+	issue = {19},
+	pages = {197203},
+	numpages = {7},
+	year = {2016},
+	month = {Nov},
+	publisher = {American Physical Society},
+	doi = {10.1103/PhysRevLett.117.197203},
+	url = {https://link.aps.org/doi/10.1103/PhysRevLett.117.197203},
+}
+
+
+@article{Klyushina2021,
+	title = {Signatures for Berezinskii-Kosterlitz-Thouless critical behavior in
+	         the planar antiferromagnet ${\mathrm{BaNi}}_{2}{\mathrm{V}}_{2}{
+	         \mathrm{O}}_{8}$},
+	author = {Klyushina, E. S. and Reuther, J. and Weber, L. and Islam, A. T. M.
+	          N. and Lord, J. S. and Klemke, B. and M\aa{}nsson, M. and Wessel,
+	          S. and Lake, B.},
+	journal = {Phys. Rev. B},
+	volume = {104},
+	issue = {6},
+	pages = {064402},
+	numpages = {14},
+	year = {2021},
+	month = {Aug},
+	publisher = {American Physical Society},
+	doi = {10.1103/PhysRevB.104.064402},
+	url = {https://link.aps.org/doi/10.1103/PhysRevB.104.064402},
+}
+
+@article{Earl2005,
+	author = "Earl, David J. and Deem, Michael W.",
+	title = "Parallel tempering: Theory{,} applications{,} and new perspectives",
+	journal = "Phys. Chem. Chem. Phys.",
+	year = "2005",
+	volume = "7",
+	issue = "23",
+	pages = "3910-3916",
+	publisher = "The Royal Society of Chemistry",
+	doi = "10.1039/B509983H",
+	url = "http://dx.doi.org/10.1039/B509983H",
+	abstract = "We review the history of the parallel tempering simulation
+	            method. From its origins in data analysis{,} the parallel
+	            tempering method has become a standard workhorse of
+	            physicochemical simulations. We discuss the theory behind the
+	            method and its various generalizations. We mention a selected set
+	            of the many applications that have become possible with the
+	            introduction of parallel tempering{,} and we suggest several
+	            promising avenues for future research.",
+}
+
+@article{Matsumoto1998,
+	author = {Matsumoto, Makoto and Nishimura, Takuji},
+	title = {Mersenne twister: a 623-dimensionally equidistributed uniform
+	         pseudo-random number generator},
+	year = {1998},
+	issue_date = {Jan. 1998},
+	publisher = {Association for Computing Machinery},
+	address = {New York, NY, USA},
+	volume = {8},
+	number = {1},
+	issn = {1049-3301},
+	url = {https://doi.org/10.1145/272991.272995},
+	doi = {10.1145/272991.272995},
+	abstract = {A new algorithm called Mersenne Twister (MT) is proposed for
+	            generating uniform pseudorandom numbers. For a particular choice
+	            of parameters, the algorithm provides a super astronomical period
+	            of 219937 −1 and 623-dimensional equidistribution up to 32-bit
+	            accuracy, while using a working area of only 624 words. This is a
+	            new variant of the previously proposed generators, TGFSR,
+	            modified so as to admit a Mersenne-prime period. The
+	            characteristic polynomial has many terms. The distribution up to
+	            v bits accuracy for 1 ≤ v ≤ 32 is also shown to be good. An
+	            algorithm is also given that checks the primitivity of the
+	            characteristic polynomial of MT with computational complexity
+	            O(p2) where p is the degree of the polynomial.We implemented this
+	            generator in portable C-code. It passed several stringent
+	            statistical tests, including diehard. Its speed is comparable to
+	            other modern generators. Its merits are due to the efficient
+	            algorithms that are unique to polynomial calculations over the
+	            two-element field.},
+	journal = {ACM Trans. Model. Comput. Simul.},
+	month = jan,
+	pages = {3–30},
+	numpages = {28},
+	keywords = {tempering, random number generation, primitive polynomials,
+	            multiple-recursive matrix method, inversive-decimation method,
+	            incomplete array, finite fields, TGFSR, Mersenne twister,
+	            Mersenne primes, MT19937, GFSR, m-sequences, k-distribution},
+}
+
+  
+
+@article{Sandvik2010,
+	author = {Sandvik, Anders W.},
+	title = {Computational Studies of Quantum Spin Systems},
+	journal = {AIP Conference Proceedings},
+	volume = {1297},
+	number = {1},
+	pages = {135-338},
+	year = {2010},
+	month = {11},
+	abstract = {These lecture notes introduce quantum spin systems and several
+	            computational methods for studying their ground‐state and
+	            finite‐temperature properties. Symmetry‐breaking and critical
+	            phenomena are first discussed in the simpler setting of Monte
+	            Carlo studies of classical spin systems, to illustrate
+	            finite‐size scaling at continuous and first‐order phase
+	            transitions. Exact diagonalization and quantum Monte Carlo
+	            (stochastic series expansion) algorithms and their computer
+	            implementations are then discussed in detail. Applications of the
+	            methods are illustrated by results for some of the most essential
+	            models in quantum magnetism, such as the S = 1/2 Heisenberg
+	            antiferromagnet in one and two dimensions, as well as extended
+	            models useful for studying quantum phase transitions between
+	            antiferromagnetic and magnetically disordered states.},
+	issn = {0094-243X},
+	doi = {10.1063/1.3518900},
+	url = {https://doi.org/10.1063/1.3518900},
+	eprint = {https://pubs.aip.org/aip/acp/article-pdf/1297/1/135/11407753/135\_
+	          1\_online.pdf},
+}
+
+
+@article{Wolff1989,
+	title = {Collective Monte Carlo Updating for Spin Systems},
+	author = {Wolff, Ulli},
+	journal = {Phys. Rev. Lett.},
+	volume = {62},
+	issue = {4},
+	pages = {361--364},
+	numpages = {0},
+	year = {1989},
+	month = {Jan},
+	publisher = {American Physical Society},
+	doi = {10.1103/PhysRevLett.62.361},
+	url = {https://link.aps.org/doi/10.1103/PhysRevLett.62.361},
+}
+
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diff --git a/paper/paper.tex b/paper/paper.tex
index 724aac8..684b550 100644
--- a/paper/paper.tex
+++ b/paper/paper.tex
@@ -25,6 +25,8 @@
 \usepackage{float}
 \usepackage{physics}
 \usepackage{braket}
+\usepackage{microtype}
+\usepackage{inconsolata}
 \input{julia_style}
 \urlstyle{same}
 
@@ -40,6 +42,8 @@
 \fancyfoot[C]{\textbf{\thepage}}
 }
 
+\newcommand\banivo{BaNi\textsubscript{2}V\textsubscript{2}O\textsubscript{8}}
+
 \begin{document}
 
 \pagestyle{SPstyle}
@@ -100,15 +104,15 @@ \section{Introduction}
 
 The Julia programming language~\cite{Bezanson2012} is becoming increasingly popular as an alternative to traditional scientific computing languages such as C++ and Fortran. Its heavy reliance on type inference, dynamic dispatch, and just-in-time compilation allow it to provide both high performance and the flexibility of a high-level scripting language. Furthermore, its modern approach to dependency management greatly facilitates installing and reusing existing software.
 
-The purpose of Carlo.jl is to provide a high-performance Monte Carlo framework for Julia. Its features include (i) Monte Carlo aware parallel scheduling (ii) organized and reproducible storage of simulation inputs, checkpoints, and results, as well as (iii) statistical postprocessing of autocorrelated Monte Carlo samples.
+The purpose of Carlo.jl is to help implementers of Monte Carlo codes in Julia to write high-quality, high-performance packages without worrying about the peripheral bookkeeping tasks that are common to all Monte Carlo simulations. Its features include (i) Monte Carlo aware parallel scheduling (including parallel tempering) (ii) organized and reproducible storage of simulation inputs, checkpoints, and results, as well as (iii) statistical postprocessing of autocorrelated Monte Carlo samples.
 
-In \cref{sec:features}, the features of Carlo.jl and their inner workings are explained in detail. \cref{sec:ising} showcases how to implement a Monte Carlo code in Carlo.jl using the paradigmatic Metropolis Monte Carlo algorithm for the Ising model as an example. Finally, in \cref{sec:conclusion}, a short conclusion and outlook are given.
+In \cref{sec:features}, the features of Carlo.jl and their inner workings are explained in detail. \cref{sec:examples} contains three examples: an Ising code that provides a minimal skeleton for implementing Monte Carlo algorithms in Carlo.jl, a state-of-the-art stochastic series expansion Monte Carlo code~\cite{Sandvik1999}, and an example of the parallel tempering feature. Afterwards, in \cref{sec:benchmarks}, we show correctness and performance benchmarks of Carlo.jl, including a direct performance comparison of a Julia and a C++ implementation of the stochastic series expansion code. Finally, in \cref{sec:conclusion}, a short conclusion and outlook are given.
 
 Apart from this user guide, users may refer to the Carlo.jl documentation\footnote{The documentation can be viewed online on \href{https://github.com/lukas-weber/Carlo.jl.git}{GitHub}, built locally by running  \texttt{cd docs; julia ----project make.jl}, or accessed directly within the Julia REPL.} for more detailed descriptions of each component.
 
 \section{Features}
 \label{sec:features}
-The purpose of this section is to give a high-level overview of the way Carlo.jl works without descending too far into technical details and concrete usage instructions. For a more hands-on introduction into how to use Carlo.jl in practice, see \cref{sec:ising}.
+The purpose of this section is to give a high-level overview of the way Carlo.jl works without descending too far into technical details and concrete usage instructions. For a more hands-on introduction into how to use Carlo.jl in practice, see \cref{sec:examples}.
 \subsection{Monte Carlo aware parallel scheduling}
 One useful property of Monte Carlo simulations is that they are embarrassingly parallel. An arbitrary number of random processes can be allocated to many workers in parallel, which, once thermalized, can all produce samples that are finally averaged together. Apart from this intrinsic parallelism, simulations are often run for a variety of different parameters in parallel.
 \begin{figure}
@@ -120,7 +124,7 @@ \subsection{Monte Carlo aware parallel scheduling}
 
 Carlo.jl uses MPI.jl~\cite{Byrne2021} to orchestrate this kind of Monte Carlo aware, work-sharing scheduling and automatically averages the results. Each parameter set in the simulation corresponds to a \textit{task} and each task may have multiple \textit{runs}, which correspond to independent random processes that are averaged. If workers are idle, the scheduler will assign them a new task from the set of unfinished tasks in a round-robin manner and start a new run for that task, provided the remaining work is not less that the number of thermalization sweeps.
 
-On top of this model of trivial parallelism, Carlo.jl also supports nontrivial MPI parallelism. The work of each run may optionally be shared by more than one MPI rank. This advanced feature, called \textit{parallel run mode}, can be helpful in situations where the runtime of a simulation is dominated by the thermalization steps. It also allows the natural implementation of branching random walk algorithms on top of Carlo.jl. While the Ising example will not use this feature, further information on how to use parallel run mode is available in the documentation.
+On top of this model of trivial parallelism, Carlo.jl also supports nontrivial MPI parallelism: The work of each single run may optionally be shared by a team of MPI ranks. This advanced feature, called \textit{parallel run mode} allows the natural implementation of certain Monte Carlo meta-techniques such as parallel tempering, which will be illustrated in \cref{sec:parallel_tempering}. Another possible use case is the implementation of branching-random walk codes that propagate an population of walkers in parallel.
 \subsection{Organized storage of inputs, checkpoints and results}
 As mentioned in the previous section, large-scale Monte Carlo simulations can involve scanning large parameter spaces and produce large numbers of random samples. Long-running simulations should also implement some form of checkpointing so that valuable computation time is not wasted when an error occurs or the job runs out of its allocated runtime on a computing cluster. 
 
@@ -163,7 +167,6 @@ \subsubsection{Input}
 \caption{\textbf{Carlo job script}. This snippet generates a job for the Ising code implemented in \cref{sec:ising}. Arbitrary parameters can be assigned to the \texttt{TaskMaker} \texttt{tm}. The function \texttt{task(tm)} creates a snapshot of all currently set values and turns it into a task that will be simulated. The list of tasks is returned by \texttt{make\_{}tasks} and passed to the \texttt{JobInfo} structure. The detailed meanings of the options are explained in \cref{sec:ising}.}
 \label{code:input}
 \end{lstfloat}
-
 The CLI allows \textit{running} the simulation, and for unfinished simulations allows checking their \textit{status} and \textit{merging} the already available data to obtain preliminary results. 
 
 While recommended, the use of \texttt{TaskMaker} and the CLI is optional. For more information on how to manually start simulations from within Julia, interested readers are referred to the documentations of \texttt{JobInfo} and the \texttt{start} function.
@@ -205,7 +208,16 @@ \subsection{Postprocessing}
 
  Apart from the observables themselves, users can also define \textit{evaluables} that depend on the observables via some function. The bias-corrected means and errors for evaluables are then 
 propagated using the jackknife~\cite{Miller1974} method on the rebinned samples.
-\section{Usage example: Ising model}
+\section{Examples}
+\label{sec:examples}
+The specifics of implementing and running codes with Carlo.jl are best explained using examples. In the following, we will show three examples, in raising complexity.
+
+The first example, \cref{sec:ising}, will be the paradigmatic Metropolis Monte Carlo algorithm for the Ising model. While this algorithm itself is very simple and of limited use in practice, it provides a minimal skeleton for implementing new Monte Carlo algorithms in Carlo.jl without the distractions of method-specific details.
+
+The second example, \cref{sec:sse}, will be an implementation of the stochastic series expansion Monte Carlo~\cite{Sandvik1999} approach on top of Carlo.jl. While this implementation is a separate package and we will not go into details about its inner workings, it here serves to show how Carlo.jl is useful in state-of-the-art Monte Carlo calculations. This will be supplemented in \cref{sec:benchmarks} by a benchmark directly comparing Julia and C++ performance for that code.
+
+The last example, \cref{sec:parallel_tempering}, will have a split purpose. First, it will introduce the parallel-tempering feature that is included in Carlo.jl. Second, it will show how parallel-tempering was implemented as a simple wrapper on top of the parallel run mode feature.
+\subsection{Ising model}
 \label{sec:ising}
 In this section, we will give a hands-on usage example for Carlo.jl by implementing and running the Metropolis Monte Carlo algorithm~\cite{Metropolis1953} for the Ising model on a square lattice,
 \begin{equation}
@@ -214,7 +226,7 @@ \section{Usage example: Ising model}
 with periodic boundary conditions.
 All code for this example is available in a separate repository~\cite{IsingExample}.
 
-\subsection{Implementation}
+\subsubsection{Implementation}
 First, we need to implement the algorithm. It is a good idea to write such an implementation as its own Julia package. In the following, we will assume that we have generated a package called \texttt{Ising}, with a file \texttt{Ising.jl} containing all the code.
 
 In this file, we declare a new subtype of \texttt{AbstractMC}.
@@ -320,7 +332,7 @@ \subsection{Implementation}
 The next method is optional, but can be used to register \textit{evaluables}, that is, quantities that depend on Monte Carlo expectation values. Carlo.jl will perform error-propagation and bias correction on these (see~\cref{sec:postproc}).
 \begin{lstlisting}[language=julia]
 function Carlo.register_evaluables(
-	::Type{MC}, eval::Evaluator, params::AbstractDict
+	::Type{MC}, eval::AbstractEvaluator, params::AbstractDict
 )
     T = params[:T]
     Lx = params[:Lx]
@@ -367,9 +379,17 @@ \subsection{Implementation}
 
 This concludes the \texttt{Ising.jl} file and our implementation. Next, we will use it to run some simulations.
 
-\subsection{Running simulations}
-In an environment, where we have access to the \texttt{Ising} module,\footnote{For example, we can add the module to environment using \texttt{]dev path/to/Ising} in the Julia REPL.} we write the job script from \cref{code:input}. The meanings of the parameters are as follows.
+\subsubsection{Running simulations}
+\label{sec:runising}
+To run a simulation, we first need to install Carlo.jl and the Ising module. This works via the Julia REPL.
+\begin{lstlisting}
+julia>]
+pkg> add Carlo
+pkg> add https://github.com/lukas-weber/Ising.jl
+\end{lstlisting}
+Readers who have followed along in the last section and wrote their own code in a different directory, can instead import it in development mode using \texttt{dev path/to/Ising}.
 
+Next, we write the job script from \cref{code:input}. The meanings of the parameters are as follows.
 \begin{description}
 \item[\texttt{Lx}, \texttt{Ly}, \texttt{T}] used by our implementation to set the size and temperature of the Ising model.
 \item[\texttt{thermalization}] the number of sweeps that are performed in the thermalization phase of the simulation, before measurements are taken.
@@ -388,7 +408,8 @@ \subsection{Running simulations}
 The first line gives an overview over the CLI, the second line starts the simulation.
 For long-running simulations, the commands \texttt{status} and \texttt{merge} are helpful to check the progress and postprocess those results that are already available, respectively.
 
-Once the simulation completes, next to the job script, we should see a directory \texttt{example\_{}job.data}, which contains raw data and check points, and a file \texttt{example\_{}job.results.json}, which contains the postprocessed results of our simulation. The submodule \texttt{Carlo.ResultTools} provides tools for reading these results back into Julia.
+After the simulation has completed, we should see a directory \texttt{example\_{}job.data}, which contains raw data and check points, and a file \texttt{example\_{}job.results.json}, which contains the postprocessed results of our simulation.
+The submodule \texttt{Carlo.ResultTools} provides tools for reading these results back into Julia.
 \begin{lstlisting}[language=julia]
 using Plots
 using DataFrames
@@ -416,7 +437,7 @@ \subsection{Running simulations}
 to retrieve a vector containing each recorded sample of the energy.
 \begin{figure}
 \begin{center}
-\includegraphics[scale=0.6]{figs/binder_ratio.pdf}
+\includegraphics[scale=0.625]{figs/binder_ratio.pdf}
 \end{center}
 \caption{\textbf{Binder ratio}, $\braket{m^2}^2/\braket{m^4}$, of the magnetization $m$, in the $L\times L$ square-lattice Ising model as a function of temperature. As one would expect, there is a crossing close to the critical temperature $T_c \approx 2.269$. The error bars are calculated automatically by Carlo.jl using the jackknife method.}
 \label{fig:binder}
@@ -440,8 +461,367 @@ \subsection{Running simulations}
 \end{lstlisting}
 Further, by default, Julia will use multithreading for linear algebra operations. Without care, together with MPI parallelization, this can cause overusage of the available CPUs, so 
 it should be controlled, e.g. by setting the environment variable \texttt{OPENBLAS\_{}NUM\_{}THREADS=1}.
- 
+\subsection{Stochastic series expansion}
+\label{sec:sse}
+In the last section, we covered the Metropolis algorithm for the Ising magnet. More complicated models of magnetism -- or other quantum phenomena -- generally contain noncommuting operators, which require more sophisticated quantum Monte Carlo algorithms to solve. One quantum Monte Carlo method that is particularly effective for lattice models of bosons is the stochastic series expansion~\cite{Sandvik1999}. In basic terms, it works by expanding the trace over Boltzmann operator $Z=\Tr e^{-\beta H}$ with the Hamiltonian $H$ and the inverse temperature $\beta$ into a power series and performing the resulting sums over over operator products using Monte Carlo sampling. More details can be found, e.g. in Ref.~\cite{Sandvik2010}.
+
+StochasticSeriesExpansion.jl~\cite{WeberStochasticSeriesExpansion2024} is an implementation of the abstract-loop flavor\cite{Weber2022} of the algorithm that can flexibly handle any model consisting of bond operators acting on a graph of bonds (as long as the sign problem~\cite{Pan2024} is not severe). It is built in Julia on top of Carlo.jl, based on the C++ code that was used in earlier publications to simulate frustrated magnets in cluster bases~\cite{Jimenez2021,WeberCluster2022,WeberThermal2022} and spin-photon coupled systems~\cite{weber_cavityrenormalized_2023}.
+
+While this arbitrary model capability requires some code to specify the Hamiltonians and associated observables, some models are supported out of the box. One example, that we will explore in this section are arbitrary-spin anisotropic Heisenberg models of the form
+\begin{equation}
+\label{eq:heisenberg}
+H = \sum_{\braket{i,j}} J_{ij} \qty(\vb S_i \cdot \vb S_j + d_{ij} S^z_i S^z_j) + \sum_i h_i^z S^z_i + D^x_i (S^x_i)^2 + D^z_i (S^z_i)^2,
+\end{equation}
+where $\braket{i,j}$ sums over the bonds of an arbitrary lattice. As long as the signs of $J_{ij}$ in combination with the bonds of the lattice do not imply magnetic frustration, the model is sign-problem free. This is the case, e.g., for $J_{ij} > 0$ on a bipartite lattice.
+
+As a registered package, we can install StochasticSeriesExpansion.jl (and Carlo.jl if we have not already) from the Julia REPL.
+\begin{lstlisting}
+julia>]
+pkg> add StochasticSeriesExpansion
+\end{lstlisting}
+Then we can write a job script. In this example, we calculate the susceptibility of an effective model for the anisotropic antiferromagnet \banivo from Ref.~\cite{Klyushina2021}, which is also available as an example in the StochasticSeriesExpansion.jl documentation.
+\begin{lstlisting}[language=julia]
+# bani2v2o8.jl
+
+using Carlo
+using Carlo.JobTools
+using StochasticSeriesExpansion
+
+tm = TaskMaker()
+tm.sweeps = 80000
+tm.thermalization = 10000
+tm.binsize = 100
+
+temperatures = range(0.05, 4, 20)
+system_sizes = [10, 20]
+
+tm.model = MagnetModel
+tm.S = 1
+tm.J = 1
+tm.Dz = 0.005645 # D^{QMC}_{EP(XY)}/J^{QMC}_n from PRB 104, 065502 
+
+tm.measure = [:magnetization]
+for L in system_sizes
+    tm.lattice = (unitcell = UnitCells.honeycomb, size = (L, L))
+
+    for T in temperatures
+        tm.T = T
+        task(tm)
+    end
+end
+
+job = JobInfo(
+    splitext(@__FILE__)[1],
+    StochasticSeriesExpansion.MC;
+    run_time = "24:00:00",
+    checkpoint_time = "30:00",
+    tasks = make_tasks(tm),
+)
+
+start(job, ARGS)
+\end{lstlisting}
+The meanings of the StochasticSeriesExpansion.jl-specific parameters are the following
+\begin{description}
+\item[\texttt{model}] the model to simulate, here \texttt{MagnetModel} which corresponds to \cref{eq:heisenberg}.
+\item[\texttt{S}] the spin magnitude
+\item[\texttt{T}] the temperature
+\item[\texttt{J,d,h,Dx,Dz}] correspond to the parameters in \cref{eq:heisenberg}. Can also be made site-dependent, see StochasticSeriesExpansion.jl documentation.
+\item[\texttt{lattice}] the unitcell and the dimensions of the supercell. Honeycomb and other popular ones are predefined. Otherwise, an instance of \texttt{UnitCell} can be passed.
+\item[\texttt{measure}] specifies the observables to be measured (on top of the energy and specific heat). Here, just measure uniform magnetization-related quantities. \texttt{:staggered\_{}magnetization} would additionally compute the staggered magnetization. There is an operator string estimator interface for implementing custom observable estimators.
+\end{description}
+For details, the reader is referred to the StochasticSeriesExpansion.jl documentation.
+
+Even though the runtime scaling of stochastic series expansion is linear in system size and inverse temperature, this example takes more computational effort than the previous one for the Ising model. It is therefore recommended to run it with MPI.
+\begin{lstlisting}
+$ mpirun -n $ncores julia example_job.jl run
+\end{lstlisting}
+Nevertheless, it is still tractable within a few minutes on a workstation or strong laptop and should yield the result file \texttt{bani2v2o8.result.json}. Like in the Ising example, we can use \texttt{Carlo.ResultTools} to plot the observable \texttt{MagChi} which corresponds to the static uniform magnetic susceptibility \cref{fig:susceptibility}.
+\begin{figure}
+\begin{center}
+\includegraphics[scale=0.625]{figs/bani2v2o8.pdf}
+\end{center}
+\caption{\textbf{Example calculation with StochasticSeriesExpansion.jl}. The magnetic susceptibility perpendicular to the easy plane, $\chi^z$, of an effective model for \banivo, as a function of the temperature $T$.}
+\label{fig:susceptibility}
+\end{figure}
+
+We observe the dip feature that is caused by the easy-plane anisotropy $D^z$ and is also observed in experiment~\cite{Klyushina2021}. However, this feature is not quite converged with system size at $L=20$ and larger systems should be simulated in practice.
+
+This concludes the present example, which showcases the effectiveness of a state-of-the-art Monte Carlo code built on Carlo.jl. Since this code was ported from an earlier C++ version, it also gives us an opportunity to directly compare the performance between the two languages, which we will do in \cref{sec:benchmarks}.
+\subsection{Parallel tempering and the parallel run mode}
+\label{sec:parallel_tempering}
+Parallel tempering~\cite{Earl2005} is a technique that allows speeding up autocorrelation times in an ensemble of simulations by introducing additional Monte Carlo moves that exchange configurations between different simulation parameters. A typical application of this are glassy models, which can be simulated ergodically at high temperatures but freeze at low temperatures. If we simulate a chain of increasing temperatures in parallel, the probability distributions of adjacent temperatures may have some overlap so that higher temperature configurations may be accepted as updates in lower temperature simulations and vice versa. This leads to a steady exchange of configurations up and down the chain of temperatures, which can decrease the overall autocorrelation time significantly.
+
+Carlo supports parallel tempering through the \texttt{ParallelTemperingMC} wrapper, which is a meta-implementation of the \texttt{AbstractMC} interface that allows to run other implementations with parallel tempering. We will first illustrate its usage with an example that is of interest to readers planning to use parallel tempering. Afterwards, we sketch its implementation as an example for implementing new algorithms with the parallel run mode feature in Carlo.jl.
+\subsubsection{Usage}
+Parallel tempering can be used with any implementation of the \texttt{AbstractMC} interface as long as it implements two additional functions,
+\begin{lstlisting}[language=julia]
+Carlo.parallel_tempering_log_weight_ratio(
+    mc::MC, parameter::Symbol, new_value
+)
+
+Carlo.parallel_tempering_change_parameter!(
+    mc::MC, parameter::Symbol, new_value
+)
+\end{lstlisting}
+Both of them receive the name of the \texttt{parameter} along which parallel tempering is performed. In a tempering update, this parameter may be changed to a \texttt{new\_{}value}. The first function returns the logarithmic weight change $\log[W(p')/W(p)]$ that would result from changing the \texttt{parameter} from $p$ to $p'$. The second function puts that same change into action. Both the Ising reference implementation and \texttt{StochasticSeriesExpansion.jl} implement this interface and can be used with \texttt{ParallelTemperingMC}.
+
+Parallel tempering is useful in situations where the untempered autocorrelation time of a simulation is longer than the time it takes to exchange replicas in the tempering process. Such a situation is not easy to achieve for the SSE algorithm in standard models due to its efficient global loop updates, but can be useful in more involved situations~\cite{Torres2020}. To keep the presentation of this usage example transparent, we will not introduce an involved model here and instead return to the Ising reference implementation that only contains local updates and is therefore known to have long autocorrelation times around the critical point.
+
+Using \texttt{ParallelTemperingMC} requires just a few changes to the job script of \cref{code:input},
+\begin{lstlisting}[language=Julia]
+# parallel_tempering.jl
+
+using Carlo
+using Carlo.JobTools
+using Ising
+
+tm = TaskMaker()
+
+tm.sweeps = 20000
+tm.thermalization = 2000
+tm.binsize = 100
+
+Ts = range(1.5, 4, 30)
+
+# contract temperatures around Tc for better distribution overlap
+Tc = 2.269
+Ts += 0.5 .* (Tc .- Ts) ./ (0.6 .+ (Tc .- Ts) .^ 2)
+
+
+tm.parallel_tempering = (
+    mc = Ising.MC,
+    parameter = :T,
+    values = Ts,
+    interval = 1
+)
+
+Ls = [32, 64]
+for L in Ls
+    tm.Lx = L
+    tm.Ly = L
+
+    # tm.T is set implicitly by ParallelTemperingMC
+
+    task(tm)
+end
+
+job = JobInfo(
+    splitext(@__FILE__)[1],
+    ParallelTemperingMC; # underlying MC set in tm.parallel_tempering
+    run_time = "24:00:00",
+    checkpoint_time = "30:00",
+    tasks = make_tasks(tm),
+    ranks_per_run = length(tm.parallel_tempering.values), # needs to match!
+)
+
+start(job, ARGS)
+\end{lstlisting}
+Most notably, we replace the MC algorithm in \texttt{JobInfo} by \texttt{ParallelTemperingMC} and use the parameter \texttt{tm.parallel\_{}tempering} to specify the details of how parallel tempering should be performed as follows
+\begin{description}
+\item[\texttt{mc}] the underlying model MC implementation.
+\item[\texttt{parameter}] name of the parameter along which parallel tempering is performed, e.g. \texttt{:T} for the temperature.
+\item[\texttt{values}] a chain of values of the parameter, which is simulated in parallel with nearest neighbor replica exchange.
+\item[\texttt{interval}] the number of sweeps between proposing replica exchanges.
+\end{description}
+Lastly, \texttt{ParallelTemperingMC} has to be run in parallel run mode, which as of Carlo v0.2.3 has to be enabled manually by setting the \texttt{ranks\_{}per\_{}run} option in \texttt{JobInfo}. In the case of \texttt{ParallelTemperingMC}, the number of ranks per run has to be set to the number of parameters in the parallel tempering chain.
+
+Running the job script works just as in the previous examples,
+\begin{lstlisting}
+$ mpirun -n $N julia parallel_tempering.jl run
+\end{lstlisting}
+except running with MPI is required and the number of MPI ranks $N$ has to be equal to \texttt{m * ranks\_{}per\_{}run + 1} with some integer $m$. For the example above, $N=61$ will simulate the two length-30 parallel tempering chains for $L=32$ and $L=64$ in parallel.
+
+As shown in \cref{fig:parallel_tempering}, in this case, parallel tempering greatly decreases the statistical uncertainties close to the critical point and cures thermalization issues that arise at low temperatures. It should be mentioned that in the case of the Ising model, the critical slowing down can be more efficiently cured by introducing cluster updates~\cite{Wolff1989}. However, designing such global updates is not always possible for more complicated models.
+
+\begin{figure}
+\begin{center}
+\includegraphics{figs/parallel_tempering.pdf}
+\end{center}
+\caption{\textbf{Parallel tempering in the Ising model.} The specific heat of the $64 \times 64$ square lattice Ising model as a function of the temperature, simulated with and without parallel tempering. Both simulations are perfored with 20000 measurement sweeps and 2000 thermalization sweeps.}
+\label{fig:parallel_tempering}
+\end{figure}
+
+\subsubsection{Implementation}
+In the last subsection, we explained the usage of the parallel tempering feature. Now, we will now sketch its underlying implementation as an example of writing an algorithm with the parallel run mode feature of Carlo.jl.
+
+In general, introducing parallel tempering into a simulation greatly increases the complexity of the parallel scheduling, since multiple simulations need to be orchestrated to run in lock step. However, Carlo.jl already supports this kind of parallelism through its parallel run mode. Parallel tempering (and similar meta-algorithms) can therefore be implemented as a thin layer on top of parallel run mode. 
+
+To use parallel run mode, algorithms have to implement an alternative version of the \texttt{AbstractMC} interface, which essentially receives an additional MPI communicator (\cref{tab:parallelinterface}) that spans a team of MPI ranks that are collaborating on a single Carlo.jl run (that is, a single bar in \cref{fig:mcsched}).
+\begin{table}
+\begin{tabular}{l}
+\hline
+\textbf{Single run interface}\\
+\hline
+\texttt{MC(parameters::AbstractDict)}  \\
+\texttt{init!(::MC, ::MCContext, params::AbstractDict)}\\
+\texttt{sweep!(::MC, ::MCContext)}\\
+\texttt{measure!(::MC, ::MCContext)}\\
+\texttt{register\_{}evaluables(::Type{MC}, ::AbstractEvaluator, params::AbstractDict)}\\
+\texttt{write\_{}checkpoint(::MC, ::HDF5.Group)}\\
+\texttt{read\_{}checkpoint!(::MC, ::HDF5.Group)}\bigskip\\
+\hline
+\textbf{Parallel run interface}\\
+\hline
+\texttt{MC(parameters::AbstractDict)}$^*$\\
+\texttt{init!(::MC, ::MCContext, params::AbstractDict, comm::MPI.Comm)}\\
+\texttt{sweep!(::MC, ::MCContext, comm::MPI.Comm)}\\
+\texttt{measure!(::MC, ::MCContext, comm::MPI.Comm)}$^{\dag}$\\
+\texttt{register\_{}evaluables(::Type\{MC\}, ::AbstractEvaluator, params::AbstractDict)}\\
+\texttt{write\_{}checkpoint(::MC, ::Union\{HDF5.Group,Nothing\}, comm::MPI.Comm)}$^\dag$\\
+\texttt{read\_{}checkpoint!(::MC, ::Union\{HDF5.Group,Nothing\}, comm::MPI.Comm)}$^\dag$\\
+\end{tabular}
+\caption{Comparison between the standard single run interface for a type \texttt{MC <: AbstractMC}, where one Carlo.jl \textit{run} (i.e. one simulation of a single parameter set) is handled by one MPI rank, to the parallel run interface, where the work of one run is shared among a team of MPI ranks. The communicator \texttt{comm} passed as an additional argument spans this team of ranks. $^*$The constructor has the same signature, but additionally, \texttt{params[:\_{}comm]} contains the MPI communicator. $^\dag$In these methods, only the 0th rank of \texttt{comm} is allowed to call \texttt{measure!(ctx,...)}, read, or write to HDF5. The second argument of the checkpointing functions is \texttt{nothing} on the other ranks.}
+\label{tab:parallelinterface}
+\end{table}
+In the parallel tempering scenario, we thus assign one chain of the tempered parameter to one Carlo run, and write a meta-implementation of the parallel run \texttt{AbstractMC} interface that runs the simulations for each value of the parameter.
+
+\begin{lstlisting}[language=julia]
+mutable struct ParallelTemperingMC{T} <: AbstractMC
+    parameter_name::Symbol
+    parameter_values::Vector{T}
+    tempering_interval::Int
+
+    parallel_measure::ParallelMeasurements
+    chain_idx::Int
+    child_mc::AbstractMC
+end
+\end{lstlisting}
+The name of the tempered parameter is stored in \texttt{parameter\_{}name} with the values stored in \texttt{parameter\_{}values}. Tempering updates are performed every \texttt{tempering\_{}interval} sweeps, and \texttt{ParallelMeasurements} is a helper object for performing distributed measurements. Each instance of \texttt{ParallelTemperingMC} corresponds to one link in the parallel tempering chain and a single parameter value. \texttt{chain\_{}idx} stores the current position of the link and \texttt{child\_{}mc} stores a child Monte Carlo implementation that does the simulation between the tempering updates.
+
+Most of the implementation work is then to implement the interface functions and calling the respective function of the child implementation, making it believe that it is running normally. In the constructor and the initialization function, we retrieve the configuration and inject the current value of the tempering parameter into the normal parameter set before passing it on tho the child.
+\begin{lstlisting}[language=julia]
+function ParallelTemperingMC(params::AbstractDict)
+    config = params[:parallel_tempering]
+    MC = config.mc
+    tempering_interval = config.interval
+
+    comm = params[:_comm]
+    chain_idx = MPI.Comm_rank(comm) + 1
+
+    modified_params = deepcopy(params)
+    modified_params[config.parameter] = config.values[chain_idx]
+
+    return ParallelTemperingMC(
+        config.parameter,
+        collect(config.values),
+        config.interval,
+        ParallelMeasurements(),
+        chain_idx,
+        MC(modified_params),
+    )
+end
+
+function Carlo.init!(
+    mc::ParallelTemperingMC,
+    ctx::MCContext,
+    params::AbstractDict,
+    comm::MPI.Comm,
+)
+    modified_params = deepcopy(params)
+    modified_params[mc.parameter_name] = mc.parameter_values[mc.chain_idx]
+
+    Carlo.init!(mc.child_mc, ctx, modified_params)
+end
+\end{lstlisting}
+In the \texttt{sweep!} function we let the child do sweeps, performing a tempering update periodically.
+\begin{lstlisting}[language=julia]
+function Carlo.sweep!(
+    mc::ParallelTemperingMC, ctx::MCContext, comm::MPI.Comm
+)
+    Carlo.sweep!(mc.child_mc,
+        make_parallel_context(ctx, mc.parallel_measure))
+
+    if ctx.sweeps % mc.tempering_interval == 0
+        synchronize_measurements!(
+            ctx, mc.parallel_measure, mc.chain_idx, comm
+        )
+        tempering_update!(mc, ctx, comm)
+    end
+    return nothing
+end
+\end{lstlisting}
+The function \verb+make_parallel_context+ creates a modified \texttt{MCContext} that reroutes possible measurements using \verb+mc.parallel_measure+.
+
+Then, periodically,
+\verb+synchronize_measurements!+ performs the necessary communications that collects these measurements from different ranks and combines them into vectors in the correct order. This is necessary because in parallel run mode, only the zeroth rank of the \texttt{comm} is allowed to do measurements.
+Afterwards, \texttt{tempering\_{}update!} implements a standard neighbor swapping update~\cite{Earl2005} calling the functions \verb+parallel_tempering_log_weight_ratio+ to compare weight ratios and, if accepted, \verb+parallel_tempering_change_parameter!+ to switch the tempering parameter values. For further details, the interested reader is referred to the source code (\texttt{src/parallel\_{}tempering.jl}).
+
+For the measurements, analogously, we call the \texttt{Carlo.measure!} function on the child.
+\begin{lstlisting}[language=julia]
+function Carlo.measure!(
+    mc::ParallelTemperingMC, ctx::MCContext, comm::MPI.Comm
+)
+    Carlo.measure!(mc.child_mc,
+        make_parallel_context(ctx, mc.parallel_measure)
+    )
+end
+\end{lstlisting}
+The \texttt{register\_{}evaluables} function works the same in single run and parallel run mode. There is no MPI communication as this function is called only once per run in the postprocessing phase, after the actual simulation is already done. For the parallel tempering implementation, this still takes some bookkeeping, as we need to string together the evaluables from the child implementations in a similar way as the measurements. We will skip these details here for the sake of brevity.
+
+Finally, the checkpointing functions require some more MPI communication. The second argument in both of them is \texttt{nothing} on any rank except the zeroth rank of \texttt{comm}. We therefore communicate the state, given by the chain permutation, the parallel measurement object, and the internal state of the child implementations, before reading from or writing to the HDF5 file.
+\begin{lstlisting}[language=julia]
+function Carlo.write_checkpoint(
+    mc::ParallelTemperingMC,
+    out::Union{HDF5.Group,Nothing},
+    comm::MPI.Comm,
+)
+    chain_permutation = MPI.Gather(mc.chain_idx, comm)
+    child_mcs = MPI.gather(mc.child_mc, comm)
+    parallel_measures = MPI.gather(mc.parallel_measure, comm)
+
+    if MPI.Comm_rank(comm) == 0
+        out["chain_permutation"] = chain_permutation
+
+        for (i, (child_mc, parallel_measure)) in
+            enumerate(zip(child_mcs, parallel_measures))
+            Carlo.write_checkpoint(child_mc,
+                create_group(out, "child_mcs/$i"))
+            Carlo.write_checkpoint(parallel_measure,
+                create_group(out, "parallel_measures/$i"))
+        end
+    end
+    return nothing
+end
+
+function Carlo.read_checkpoint!(
+    mc::ParallelTemperingMC,
+    in::Union{HDF5.Group,Nothing},
+    comm::MPI.Comm,
+)
+    child_mcs = MPI.gather(mc.child_mc, comm)
+
+    if MPI.Comm_rank(comm) == 0
+        chain_permutation = read(in, "chain_permutation")
+        parallel_measures = [
+            Carlo.read_checkpoint(ParallelMeasurements,
+            in["parallel_measures/$i"])
+            for i in eachindex(child_mcs)
+        ]
+
+        for (i, child_mc) in enumerate(child_mcs)
+            Carlo.read_checkpoint!(child_mc, in["child_mcs/$i"])
+        end
+    else
+        chain_permutation = nothing
+    end
+
+    mc.chain_idx = MPI.scatter(chain_permutation, comm)
+    mc.child_mc = MPI.scatter(child_mcs, comm)
+
+    mc.parallel_measure = MPI.scatter(parallel_measures, comm)
+
+    parallel_tempering_change_parameter!(
+        mc.child_mc,
+        mc.parameter_name,
+        mc.parameter_values[mc.chain_idx],
+    )
+
+    return nothing
+end
+\end{lstlisting}
+This concludes the implementation of \texttt{ParallelTemperingMC} as an example of leveraging the parallel run mode feature. While some MPI communication and bookkeeping is required, the heavy lifting in terms of scheduling is being done behind the scenes by Carlo.jl. The main source of complexity in the parallel tempering implementation is the design requirement that it should work transparently with normal \texttt{AbstractMC} implementations. Utilities for this kind of interfacing, such as the \verb+ParallelMeasurements+ used above may also be useful for other meta-algorithms. While they are not currently part of the public Carlo.jl API, this may change in a future release.
 \section{Benchmarks}
+\label{sec:benchmarks}
 \begin{figure}
 \begin{center}
 \includegraphics{figs/scaling.pdf}
@@ -456,23 +836,98 @@ \section{Benchmarks}
 \caption{\textbf{Binning analysis benchmark} using the $20\times 20$ square-lattice Ising model at temperature $T=2.3$, close to the critical point. The same simulation with 20000 sweeps and 4000 thermalization sweeps is repeated 9000 times. We then compare the distribution of these results to the distribution predicted by the binning analysis. (a) Histogram of the energy per spin compared to a Gaussian distribution with the average mean and standard deviation predicted from the binning analysis. (b) Histogram of the Binder ratio compared to a Gaussian distribution with the average mean and standard deviation predicted from jackknifing. (c) The energy autocorrelation function, averaged over all runs, compared to the autocorrelation time $\tau_\text{auto}$ predicted by Carlo.jl.}
 \label{fig:statistics}
 \end{figure}
-In this section, we will provide benchmarks to show (i) the runtime scaling of the parallel scheduler and (ii) the validity of the statistical postprocessing in the face of strongly autocorrelated data. For both, we will use the Ising example code implemented in \cref{sec:ising}.
+In this section, we provide benchmarks to show (i) the runtime scaling of the parallel scheduler and (ii) the validity of the statistical postprocessing in the face of strongly autocorrelated data. For both, we use the Ising example code implemented in \cref{sec:ising}. Finally, we (iii) directly compare the performance of the Julia and the C++ versions of the stochastic series expansion code.
 
+\subsection{Scheduler runtime scaling}
 For the runtime scaling, we consider a workload inspired by \cref{code:input}, where we make the replacements \texttt{Ls = [100, 200, 300, 500]} and \texttt{sweeps = 200000} to increase the computational effort. Since the Ising code scales quadratically with the linear system size \texttt{Lx}, the tasks of this workload are quite imbalanced, comparable to the situation in \cref{fig:mcsched}. Nevertheless, we observe nearly linear scaling of the runtime with number CPUs used~(\cref{fig:benchmark}). We expect that the deviation from perfect scaling in this case is dominated by the serial cost of thermalization, which, based on the number of sweeps, is about 1\% of the total serial runtime.
 
+\subsection{Validity of the postprocessing}
 To confirm the accuracy of the statistical postprocessing, we consider the Ising model with $L=20$ and $T=2.3$, close to the critical point. In this region, the local updates of the Metropolis algorithm that we implemented are quite inefficient, leading to long autocorrelation times that require a careful analysis to retrieve the correct statistics.
 
 To obtain the statistics of this model, there are two ways. The first one is to run many identical, independent simulations and create a histogram of the results. The second, more practical approach is to run a single simulation and perform a binning analysis on the correlated time series. By comparing the histogram of many independent simulations with the average results from the binning analysis implemented in Carlo.jl (\cref{fig:statistics}(a)), we confirm that the binning procedure outlined in \cref{sec:postproc} yields the correct errors for observables. As an example for the jackknifing feature, the Binder ratio (\cref{fig:statistics}(b)) also shows correct statistics. Finally, in \cref{fig:statistics}(c) we show the autocorrelation function for the energy per spin. We find that the autocorrelation time estimated from the binning analysis using~\cref{eq:autocorr} is a good estimate for the true decay of the autocorrelations.
+
+\subsection{Performance comparison between Julia and C++}
+The StochasticSeriesExpansion.jl package mentioned in \cref{sec:sse} is a Julia translation of the earlier C++ code~\cite{WeberFrust2024} that was used in Refs.~\cite{Jimenez2021,Weber2022,WeberCluster2022,WeberThermal2022,weber_cavityrenormalized_2023}. Since many of its inner workings are identical and both codes have seen a similar amount of optimization efforts, they provide an ideal opportunity for benchmarking the performance of Julia for quantum Monte Carlo applications, which we do in the following.
+
+Although the codes behave identically at the core, a number of details need to be taken into account for a quantitative performance comparison. Firstly, the models implemented for use with them are not the same. For example, the anisotropic magnet from \cref{sec:sse} is not implemented in the C++ code. A model that is implemented for both is the spin-1/2 fully-frustrated bilayer~\cite{MullerHartmannExact2000,Alet2016} in the interlayer dimer basis, which we therefore use here (accessible through the \texttt{ClusterModel} in StochasticSeriesExpansion.jl). Another, more technical intricacy are the length of the SSE operator string and the number of worm updates. Both are parameters that are automatically tuned by the algorithm during its thermalization phase. Both codes use exactly the same controller logic for this, however the result is subject to noise. To eliminate this noise, we set both of them to the same values, predetermined by an earlier simulation. Lastly, the C++ version used a custom implementation of the mt19937 Mersenne Twister~\cite{Matsumoto1998}. Carlo.jl uses Julia’s \texttt{Random.Xoshiro} by default, which for this comparison, we replace by \texttt{Random.MersenneTwister}. All of these settings are implemented in the job script from \cref{lst:language_comparison}. The C++ code was compiled with GCC 12.2.0 with \texttt{-march=znver4 -ffast-math} and link-time optimization enabled. The Julia version was 1.11.1. The two simulations were carried out on AMD EPYC 9474F CPUs with 16 MPI ranks at a time.
+\begin{figure}
+\begin{center}
+\includegraphics{figs/language_comparison.pdf}
+\end{center}
+\caption{\textbf{Language performance comparison} between the Julia and C++ implementations of the same SSE QMC algorithm. Shown are the average times spent on a sweep and a measurement as a function of inverse temperature $\beta=1/T$ for the fully frustrated bilayer with interlayer to intralayer coupling ratio $J/J_\perp = 2$ and $30\times 30$ dimer unit cells. }
+\label{fig:language_comparison}
+\end{figure}
+\begin{lstfloat}
+\begin{lstlisting}[language=julia]
+using Carlo
+using Carlo.JobTools
+using StochasticSeriesExpansion
+using Random
+
+tm = TaskMaker()
+tm.sweeps = 100000
+tm.thermalization = 10000
+tm.binsize = 100
+
+tm.model = ClusterModel
+tm.inner_model = MagnetModel
+tm.cluster_bases = (StochasticSeriesExpansion.ClusterBases.dimer,)
+
+tm.measure_quantum_numbers = [(;name=Symbol(), quantum_number=2)]
+tm.parameter_map = (;
+    J = vcat([:Jperp], repeat([:Jpar],8))
+)
+
+tm.Jpar = 1
+tm.Jperp = 0.5
+
+betas = range(1,10,16)
+L = 30
+
+tm.lattice = (
+    unitcell = UnitCells.fully_frust_square_bilayer,
+    size=(L,L)
+)
+for beta in betas
+    tm.init_opstring_cutoff = 160000*beta/maximum(betas)
+    tm.init_num_worms = 8
+    tm.num_worms_attenuation_factor = 0.0
+    tm.T = 1/beta
+    tm.Lx = L
+    tm.Ly = L
+    task(tm)
+end
+
+job = JobInfo(
+    "path/to/job",
+    StochasticSeriesExpansion.MC;
+    run_time = "24:00:00",
+    checkpoint_time = "30:00",
+    rng = Random.MersenneTwister,
+    tasks = make_tasks(tm),
+)
+
+start(job, ARGS)
+\end{lstlisting}
+\caption{The StochasticSeriesExpansion.jl job file used for the performance comparison in \cref{fig:language_comparison}.}
+\label{lst:language_comparison}
+\end{lstfloat}
+
+In \cref{fig:language_comparison}, both codes show the characteristic linear scaling of the SSE algorithm with inverse temperature. The Julia version shows slightly better performance than the C++ version for both sweeps and measurements. This should not be seen as proof that one language is inherently faster or slower, as further optimizations on either side are likely possible.
+
+Some plausible explanations for the different performance could be the following. First, the sweep time could be partly affected by the different performance of the Mersenne Twister implementations. Second, due to just-in-time compilation, the Julia compiler has more compile-time knowledge. For example, both codes allow the SSE bond operators to connect an arbitrary number of sites. If the number of sites per operator is known at compile-time, which has been ensured in the Julia code, several expensive integer divisions can be replaced by cheaper bit shift operations. Achieving something similar in C++ is possible using sophisticated templating techniques, however, in the present code, this is only done in part. Lastly, the reason could be a random difference in the LLVM optimizer, used by Julia, and the GCC optimizer, used for C++ here, that happens to be relevant for the performance of the given code on the given architecture.
+
+Despite these technical details that make performance comparisons of this kind hard to interpret, we can confidently conclude that it is possible to write state-of-the-art QMC codes in Julia without paying a price in performance.
 \section{Conclusion}
 \label{sec:conclusion}
-Carlo.jl is a framework for writing Monte Carlo simulations in Julia. It features a Monte Carlo aware parallel scheduler, organized storage of input, checkpoint, and result files, as well as statistical postprocessing of the Monte Carlo results.
+Carlo.jl is a framework for writing Monte Carlo simulation codes in Julia. It features a Monte Carlo aware parallel scheduler with parallel tempering support, organized storage of input, checkpoint, and result files, as well as statistical postprocessing of the Monte Carlo results.
 
-We have illustrated these features and the general usage of the framework by providing an example implementation of the Metropolis algorithm for the Ising model. Further benchmarks, based on the example implementation have been provided to show the runtime scaling of the scheduler and the correctness of the statistical postprocessing.
+We have illustrated these features and the general usage of the framework by providing examples for the Ising model, the SSE QMC algorithm and parallel tempering. Our benchmarks show the efficient runtime scaling of the scheduler and the correctness of the statistical postprocessing. Additionally, since the SSE QMC code is based on an earlier C++ implementation, we performed a language performance comparison, in which the Julia version was faster, demonstrating the applicability of Julia for Monte Carlo workloads.
 
 Based on these features and properties, the availability of a framework like Carlo.jl should enable the quick development of new user-friendly high-performance Monte Carlo codes in Julia.
 \section*{Acknowledgements}
 Carlo.jl is inspired by an earlier C++ code~\cite{loadleveller} written by the author, which in turn was inspired by a legacy code used in Stefan Wessel's group.
-All plots except \cref{fig:binder} were created using Makie.jl~\cite{DanischKrumbiegel2021}.
+All plots except \cref{fig:binder} and \cref{fig:susceptibility} were created using Makie.jl~\cite{DanischKrumbiegel2021}.
 
 \paragraph{Funding information}
 L.W. acknowledges support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through grant WE 7176-1-1.