fitting and plotting code

cumulant_parameters.jl

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+cd(@__DIR__)
+
+using Interpolations
+using DelimitedFiles
+using StaticArrays
+using LinearAlgebra
+using LaTeXStrings
+using PlotThemes
+using Plots
+using Optim
+
+include("data/data_c2_32.jl")
+
+interp_linear1 = LinearInterpolation(t_1, c2_1)
+err_linear1 = LinearInterpolation(t_1, c2_1_err)
+
+interp_linear2 = LinearInterpolation(t_2, c2_2)
+err_linear2 = LinearInterpolation(t_2, c2_2_err)
+
+interp_linear3 = LinearInterpolation(t_3, c2_3)
+err_linear3 = LinearInterpolation(t_3, c2_3_err)
+
+
+xs = collect(-40:0.1:40)
+
+function minimize(x)
+    return sum(
+        .+ abs.(interp_linear1.(xs) .- interp_linear2.(xs*2^x[1])/2^x[2])
+        .+ abs.(interp_linear1.(xs) .- interp_linear3.(xs*4^x[1])/4^x[2])
+    )
+end
+
+initial_x=[0.7,0.3]
+res=optimize(minimize, initial_x)
+
+Optim.summary(res)
+param=Optim.minimizer(res)
+println(param)
+
+function scatter_style(xl,yl)
+    scatter!(
+        	ylabel=yl, xlabel=xl,
+            grid = :off,
+            box = :on,
+            foreground_color_legend = nothing,
+            fontfamily = "serif-roman",
+            font="CMU Serif",
+            xtickfontsize = 10,
+            ytickfontsize = 10,
+            xguidefontsize = 10,
+            yguidefontsize = 10,
+            thickness_scaling=1.5,
+            legendfontsize=10,
+            markersize=0.7,
+            legend=:topleft,
+        )
+end
+
+plotlims = (-50,100)
+xplot_1 = collect(plotlims[1]:0.1:plotlims[2])
+xplot_2 = collect(plotlims[1]*2^param[1]:0.1:plotlims[2]*2^param[1])
+xplot_3 = collect(plotlims[1]*4^param[1]:0.1:plotlims[2]*4^param[1])
+yscale(i) = interp_linear1(0) * 2^((i-1)*param[2])
+
+plot(xplot_1, interp_linear1.(xplot_1)/yscale(1), fillalpha=0.1, ribbon=err_linear1.(xplot_1)/yscale(1), label=L"\hat \tau_Q=1")
+plot!(xplot_2/2^param[1], interp_linear2.(xplot_2)/yscale(2), fillalpha=0.1, ribbon=err_linear2.(xplot_2)/yscale(2), label=L"\hat\tau_Q=2")
+plot!(xplot_3/4^param[1], interp_linear3.(xplot_3)/yscale(3), fillalpha=0.1, ribbon=err_linear3.(xplot_3)/yscale(3), label=L"\hat\tau_Q=4")
+scatter_style(L"\bar t/\hat\tau_Q^{p_1}", L"\hat c_2(\bar t,\tau_Q)/\hat \tau_Q^{p_2}")
+savefig("plots/cumulant_fit.pdf")

cumulant_plot.jl

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+cd(@__DIR__)
+
+using Plots
+using ColorSchemes
+using Statistics
+using LaTeXStrings
+using DelimitedFiles
+using LsqFit
+using Interpolations
+using Optim
+
+L = 32
+const λ = 4.0e0
+const Γ = 1.0e0
+const T = 1.0e0
+const z = 3.906e0
+
+const Δt = 0.04e0/Γ
+const Rate = Float64(sqrt(2.0*Δt*Γ))
+
+# KZ protocol variables
+const m²c, m²0, m²e = -2.28587, -2.0e0, -3.0e0
+m_a, m_b = begin
+    τ_R = 2 * 10^-3 * L^z
+    τ_Q = τ_R
+
+    m²c/τ_Q, m²0
+end
+
+# In units of time
+t_c = (m²c - m_b) / m_a
+t_e = (m²e - m_b) / m_a
+##
+
+function time_axis(m, i)
+    t = (m .- m_b) / (m_a / i)
+    t_ce = t_c * i
+    t = t / t_ce
+    t
+end
+
+function scatter_style(xl,yl)
+    scatter(
+        	ylabel=yl, xlabel=xl,
+            grid = :off,
+            box = :on,
+            foreground_color_legend = nothing,
+            fontfamily = "serif-roman",
+            font="CMU Serif",
+            xtickfontsize = 10,
+            ytickfontsize = 10,
+            xguidefontsize = 10,
+            yguidefontsize = 10,
+            thickness_scaling=1.5,
+            legendfontsize=10,
+            markersize=1,
+            legend=:topleft
+        )
+end
+
+include("data/data_c2_32.jl")
+
+p = palette(:Set1_5)
+
+df = readdlm("data/sum_1.dat", ' ')
+m_1 = df[:,2]
+df = readdlm("data/sum_2.dat", ' ')
+m_2 = df[:,2]
+df = readdlm("data/sum_3.dat", ' ')
+m_3 = df[:,2]
+
+scatter_style(L"t/t_c", L"c_2(t)")
+plot!(time_axis(m_1, 1), c2_1, fillalpha=0.1, ribbon=c2_1_err, label=L"\hat\tau_Q=1")
+plot!(time_axis(m_2, 2), c2_2, fillalpha=0.1, ribbon=c2_2_err, label=L"\hat\tau_Q=2")
+plot!(time_axis(m_3, 4), c2_3, fillalpha=0.1, ribbon=c2_3_err, label=L"\hat\tau_Q=4")
+
+savefig("plots/c2_t.pdf")

dynamic_exp.jl

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+cd(@__DIR__)
+
+using LsqFit
+using Plots
+using LaTeXStrings
+
+include("data/data_8.jl")
+include("data/data_12.jl")
+include("data/data_16.jl")
+include("data/data_24.jl")
+
+L = [8, 12, 16, 24]
+t = [t_8, t_12, t_16, t_24]
+C = [C_8, C_12, C_16, C_24]
+C_err = [Cerr_8, Cerr_12, Cerr_16, Cerr_24]
+τ = zeros(length(L))
+τ_err = zeros(length(L))
+
+for i in 1:length(L)
+    C_err[i] = C_err[i] / C[i][1]
+    C[i] = C[i] / C[i][1]
+end
+
+m(t,p) = exp.(p[1]*t)
+p0 = [-0.1]
+
+for i in 1:length(L)
+    fit = curve_fit(m, t[i], C[i], p0)
+    τ[i] = -inv(fit.param[1])
+    τ_err[i] = stderror(fit)[1]
+end
+
+fit_fn(t,p) = p[2] .+ p[1] * t
+
+z_fit = curve_fit(fit_fn, log.(L), log.(τ), [4.0, 0.0])
+(z, c) = z_fit.param
+z_err = stderror(z_fit)[1]
+
+c_err = exp(stderror(z_fit)[2])
+println(c*(1-c_err))
+
+scatter(log.(L), log.(τ), legend=:topleft, label="")
+plot!(log.(L[[1,end]]), c.+z.*log.(L[[1,end]]),
+    legend=nothing,
+    foreground_color_legend=nothing,
+    grid=:off,
+    box=:on,
+    fontfamily = "serif-roman",
+    xtickfontsize = 10,
+    ytickfontsize = 10,
+    xguidefontsize = 10,
+    yguidefontsize = 10,
+    thickness_scaling=1.5,
+    legendfontsize=5,
+    markersize=1)
+xlabel!(L"\ln\, L")
+ylabel!(L"\ln\, \tau")
+savefig("plots/z_fit_B.pdf")
+
+scatter(xlabel=L"t/L^z",
+    ylabel=L"G(t,|k|=2\pi/L)/\chi",
+    foreground_color_legend=nothing,
+    grid=:off,
+    box=:on,
+    fontfamily = "serif-roman",
+    xtickfontsize = 10,
+    ytickfontsize = 10,
+    xguidefontsize = 10,
+    yguidefontsize = 10,
+    thickness_scaling=1.5,
+    legendfontsize=10,
+    xticks = [0.0, 0.0025, 0.005, 0.0075, 0.01],
+    xlims = [0, 0.012]
+)
+
+for i in eachindex(L)
+    plot!(t[i]/L[i]^z, C[i], ribbon = C_err[i], label=L"L=%$(L[i])", fillalpha = 0.2)
+end
+
+savefig("plots/Ck1.pdf")