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-rw-r--r--autocorrelation.dat116
-rw-r--r--data/correlation-times/heisenberg-pert.dat105
-rw-r--r--data/correlation-times/heisenberg.dat93
-rw-r--r--data/correlation-times/ising-2d.dat137
-rw-r--r--data/correlation-times/ising-3d.dat111
-rw-r--r--data/correlation-times/planar-pert.dat115
-rw-r--r--data/correlation-times/planar-uni.dat46
-rw-r--r--data/correlation-times/planar.dat107
-rw-r--r--data/correlation-times/potts-3.dat120
-rw-r--r--data/correlation-times/potts-4.dat120
-rw-r--r--data/harmonic-susceptibilities/order-4.dat232
-rw-r--r--data/harmonic-susceptibilities/order-6.dat233
-rw-r--r--fig_clusters_ising2d.eps12143
-rw-r--r--fig_clusters_ising2d.tex180
-rw-r--r--fig_correlation-temp.tex4508
-rw-r--r--fig_correlation.tex3538
-rw-r--r--fig_correlation_collapse-hL.tex2098
-rw-r--r--fig_metastable.tex2340
-rw-r--r--figs/fig_correlation-times.gplot133
-rw-r--r--figs/fig_generator-times.gplot21
-rw-r--r--figs/fig_harmonic-susceptibilities.gplot37
-rw-r--r--makefile2
-rw-r--r--monte-carlo.tex12
-rw-r--r--refs/alexandrowicz1989swendsen.pdfbin937546 -> 0 bytes
-rw-r--r--refs/baillie1991comparison.pdfbin246142 -> 0 bytes
-rw-r--r--refs/coniglio1980clusters.pdfbin442501 -> 0 bytes
-rw-r--r--refs/coniglio1989exact.pdfbin463325 -> 0 bytes
-rw-r--r--refs/destri1992swendsen.pdfbin438528 -> 0 bytes
-rw-r--r--refs/dotsenko1991cluster.pdfbin172731 -> 0 bytes
-rw-r--r--refs/du2006dynamic.pdfbin602685 -> 0 bytes
-rw-r--r--refs/geyer1992practical.pdfbin1790024 -> 0 bytes
-rw-r--r--refs/hastings1970monte.pdfbin839495 -> 0 bytes
-rw-r--r--refs/janke1998nonlocal.pdfbin269280 -> 0 bytes
-rw-r--r--refs/lauwers1989critical.pdfbin195270 -> 0 bytes
-rw-r--r--refs/liu2014dynamic.pdfbin2182262 -> 0 bytes
-rw-r--r--refs/ray1990metastability.pdfbin432932 -> 0 bytes
-rw-r--r--refs/swendsen1987nonuniversal.pdfbin136908 -> 0 bytes
-rw-r--r--refs/wang1989clusters.pdfbin929783 -> 0 bytes
-rw-r--r--refs/wang1990cluster.pdfbin652558 -> 0 bytes
-rw-r--r--refs/wolff1989collective.pdfbin201013 -> 0 bytes
-rw-r--r--refs/wolff1989comparison.pdfbin279147 -> 0 bytes
-rw-r--r--refs/wolff1990critical.pdfbin945386 -> 0 bytes
42 files changed, 1623 insertions, 24924 deletions
diff --git a/autocorrelation.dat b/autocorrelation.dat
deleted file mode 100644
index d0c5af8..0000000
--- a/autocorrelation.dat
+++ /dev/null
@@ -1,116 +0,0 @@
-8 2.26918531421 0.00001 0.5835715978146659 0.008059628784399241
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-256 2.26918531421 0.0000794328 0.5776378664450701 0.07111471296548877 \ No newline at end of file
diff --git a/data/correlation-times/heisenberg-pert.dat b/data/correlation-times/heisenberg-pert.dat
new file mode 100644
index 0000000..c708670
--- /dev/null
+++ b/data/correlation-times/heisenberg-pert.dat
@@ -0,0 +1,105 @@
+L T H S dS t dt
+
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diff --git a/data/correlation-times/heisenberg.dat b/data/correlation-times/heisenberg.dat
new file mode 100644
index 0000000..17b2099
--- /dev/null
+++ b/data/correlation-times/heisenberg.dat
@@ -0,0 +1,93 @@
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diff --git a/data/correlation-times/ising-2d.dat b/data/correlation-times/ising-2d.dat
new file mode 100644
index 0000000..fe01d16
--- /dev/null
+++ b/data/correlation-times/ising-2d.dat
@@ -0,0 +1,137 @@
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diff --git a/data/correlation-times/ising-3d.dat b/data/correlation-times/ising-3d.dat
new file mode 100644
index 0000000..e036f77
--- /dev/null
+++ b/data/correlation-times/ising-3d.dat
@@ -0,0 +1,111 @@
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diff --git a/data/correlation-times/planar-pert.dat b/data/correlation-times/planar-pert.dat
new file mode 100644
index 0000000..33de73b
--- /dev/null
+++ b/data/correlation-times/planar-pert.dat
@@ -0,0 +1,115 @@
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diff --git a/data/correlation-times/planar-uni.dat b/data/correlation-times/planar-uni.dat
new file mode 100644
index 0000000..0a550ea
--- /dev/null
+++ b/data/correlation-times/planar-uni.dat
@@ -0,0 +1,46 @@
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diff --git a/data/correlation-times/planar.dat b/data/correlation-times/planar.dat
new file mode 100644
index 0000000..2d45dc5
--- /dev/null
+++ b/data/correlation-times/planar.dat
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diff --git a/data/correlation-times/potts-3.dat b/data/correlation-times/potts-3.dat
new file mode 100644
index 0000000..2024478
--- /dev/null
+++ b/data/correlation-times/potts-3.dat
@@ -0,0 +1,120 @@
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diff --git a/data/correlation-times/potts-4.dat b/data/correlation-times/potts-4.dat
new file mode 100644
index 0000000..d23d7ca
--- /dev/null
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diff --git a/data/harmonic-susceptibilities/order-4.dat b/data/harmonic-susceptibilities/order-4.dat
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diff --git a/data/harmonic-susceptibilities/order-6.dat b/data/harmonic-susceptibilities/order-6.dat
new file mode 100644
index 0000000..bf3aea3
--- /dev/null
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diff --git a/figs/fig_correlation-times.gplot b/figs/fig_correlation-times.gplot
new file mode 100644
index 0000000..7dac658
--- /dev/null
+++ b/figs/fig_correlation-times.gplot
@@ -0,0 +1,133 @@
+
+# data and constants, sorted by column
+
+isingRange = "[0.0000005:5000000]"
+
+dataIsing2D = "data/correlation-times/ising-2d.dat"
+betaIsing2D = 1.0 / 8.0
+nuIsing2D = 1.0
+deltaIsing2D = 15.0
+gammaIsing2D = 7.0 / 4.0
+zIsing2D = 0.231
+
+dataIsing3D = "data/correlation-times/ising-3d.dat"
+betaIsing3D = 0.326419
+nuIsing3D = 0.629971
+deltaIsing3D = 4.78984
+gammaIsing3D = 1.237075
+zIsing3D = 0.316
+
+pottsRange="[0.000001:5000000]"
+
+data3Potts2D = "data/correlation-times/potts-3.dat"
+beta3Potts2D = 1.0 / 9.0
+nu3Potts2D = 5.0 / 6.0
+delta3Potts2D = 14.0
+gamma3Potts2D = 13.0 / 9.0
+z3Potts2D = 0.568
+
+data4Potts2D = "data/correlation-times/potts-4.dat"
+beta4Potts2D = 1.0 / 12.0
+nu4Potts2D = 2.0 / 3.0
+delta4Potts2D = 15.0
+gamma4Potts2D = 7.0 / 6.0
+z4Potts2D = 0.953
+
+vectorRange="[0.000001:10000000]"
+
+data2Vector3D = "data/correlation-times/planar-pert.dat"
+beta2Vector3D = 0.3470
+nu2Vector3D = 0.6703
+delta2Vector3D = 4.79539
+gamma2Vector3D = 1.3169
+z2Vector3D = 0.39
+
+data3Vector3D = "data/correlation-times/heisenberg-pert.dat"
+beta3Vector3D = 0.3662
+nu3Vector3D = 0.7073
+delta3Vector3D = 4.79465
+gamma3Vector3D = 1.3895
+z3Vector3D = 0.295
+
+# define colors
+
+cc1 = "#5e81b5"
+cc2 = "#e19c24"
+cc3 = "#8fb032"
+cc4 = "#eb6235"
+cc5 = "#8778b3"
+cc6 = "#c56e1a"
+cc7 = "#5d9ec7"
+
+set palette model RGB defined ( 8 cc1, 16 cc2, 32 cc3, 64 cc4, 128 cc5, 256 cc6 , 512 cc7 )
+
+# global plotting settings
+
+set terminal epslatex size 6.834, 2.81576
+set output "fig_correlation-times.tex"
+
+set multiplot layout 2,3 margins 0.05, 0.995, 0.15, 0.99 spacing 0.05, 0.015
+set size ratio 1 / 1.61803398875
+set key autotitle columnhead
+unset colorbox
+set nokey
+set logscale xy
+
+scaledylabel = '"$\\avg{s_{\\text{\\sc 1c}}}L^{-\\gamma/\\nu}$" offset 2,0'
+
+# plotting the first row
+set format x ""
+unset xlabel
+set ylabel @scaledylabel
+
+# ploting Ising 2D
+set xrange @isingRange
+set yrange [0.2:1.1]
+
+plot dataIsing2D using (column("H")/column("T") * exp(log(column("L")) * betaIsing2D * deltaIsing2D / nuIsing2D)):(column("t") * column("S") * exp(-log(column("L")) * (zIsing2D + 2))):(sqrt((column("dt")/column("t"))**2 + (column("dS")/column("S"))**2) * column("t") * column("S") * exp(-log(column("L")) * (zIsing2D + 2))):1 with yerrorbars pt 0 lw 2 palette,\
+ dataIsing2D using (column("H")/column("T") * exp(log(column("L")) * betaIsing2D * deltaIsing2D / nuIsing2D)):(column("t") * column("S") * exp(-log(column("L")) * (zIsing2D + 2))):1 with lines palette
+
+unset ylabel
+
+# plotting 3 Potts 2D
+set xrange @pottsRange
+set yrange [0.05:2]
+
+plot data3Potts2D using (column("H")/column("T") * exp(log(column("L")) * beta3Potts2D * delta3Potts2D / nu3Potts2D)):(column("t") * column("S") * exp(-log(column("L")) * (z3Potts2D + 2))):(sqrt((column("dt")/column("t"))**2 + (column("dS")/column("S"))**2) * column("t") * column("S") * exp(-log(column("L")) * (z3Potts2D + 2))):1 with yerrorbars pt 0 lw 2 palette,\
+ data3Potts2D using (column("H")/column("T") * exp(log(column("L")) * beta3Potts2D * delta3Potts2D / nu3Potts2D)):(column("t") * column("S") * exp(-log(column("L")) * (z3Potts2D + 2))):1 with lines palette
+
+# plotting 2 Vector 3D
+set xrange @vectorRange
+set yrange [0.4:2]
+
+plot data2Vector3D using (column("H")/column("T") * exp(log(column("L")) * beta2Vector3D * delta2Vector3D / nu2Vector3D)):(column("t") * column("S") * exp(-log(column("L")) * (z2Vector3D + 3))):(sqrt((column("dt")/column("t"))**2 + (column("dS")/column("S"))**2) * column("t") * column("S") * exp(-log(column("L")) * (z2Vector3D + 3))):1 with yerrorbars pt 0 lw 2 palette,\
+ data2Vector3D using (column("H")/column("T") * exp(log(column("L")) * beta2Vector3D * delta2Vector3D / nu2Vector3D)):(column("t") * column("S") * exp(-log(column("L")) * (z2Vector3D + 3))):1 with lines palette
+
+# plotting the second row
+set format x '$10^{%T}$'
+set xlabel '$hL^{\beta\delta/\nu}$'
+set ylabel @scaledylabel
+
+# plotting Ising 3D
+set xrange @isingRange
+set yrange [0.2:1]
+
+plot dataIsing3D using (column("H")/column("T") * exp(log(column("L")) * betaIsing3D * deltaIsing3D / nuIsing3D)):(column("t") * column("S") * exp(-log(column("L")) * (zIsing3D + 3))):(sqrt((column("dt")/column("t"))**2 + (column("dS")/column("S"))**2) * column("t") * column("S") * exp(-log(column("L")) * (zIsing3D + 3))):1 with yerrorbars pt 0 lw 2 palette,\
+ dataIsing3D using (column("H")/column("T") * exp(log(column("L")) * betaIsing3D * deltaIsing3D / nuIsing3D)):(column("t") * column("S") * exp(-log(column("L")) * (zIsing3D + 3))):1 with lines palette
+
+unset ylabel
+
+# plotting 4 Potts 2D
+set xrange @pottsRange
+set yrange [0.02:4]
+
+plot data4Potts2D using (column("H")/column("T") * exp(log(column("L")) * beta4Potts2D * delta4Potts2D / nu4Potts2D)):(column("t") * column("S") * exp(-log(column("L")) * (z4Potts2D + 2))):(sqrt((column("dt")/column("t"))**2 + (column("dS")/column("S"))**2) * column("t") * column("S") * exp(-log(column("L")) * (z4Potts2D + 2))):1 with yerrorbars pt 0 lw 2 palette,\
+ data4Potts2D using (column("H")/column("T") * exp(log(column("L")) * beta4Potts2D * delta4Potts2D / nu4Potts2D)):(column("t") * column("S") * exp(-log(column("L")) * (z4Potts2D + 2))):1 with lines palette
+
+# plotting 3 Vector 3D
+set xrange @vectorRange
+set yrange [0.9:4]
+
+plot data3Vector3D using (column("H")/column("T") * exp(log(column("L")) * beta3Vector3D * delta3Vector3D / nu3Vector3D)):(column("t") * column("S") * exp(-log(column("L")) * (z3Vector3D + 3))):(sqrt((column("dt")/column("t"))**2 + (column("dS")/column("S"))**2) * column("t") * column("S") * exp(-log(column("L")) * (z3Vector3D + 3))):1 with yerrorbars pt 0 lw 2 palette,\
+ data3Vector3D using (column("H")/column("T") * exp(log(column("L")) * beta3Vector3D * delta3Vector3D / nu3Vector3D)):(column("t") * column("S") * exp(-log(column("L")) * (z3Vector3D + 3))):1 with lines palette
+
diff --git a/figs/fig_generator-times.gplot b/figs/fig_generator-times.gplot
new file mode 100644
index 0000000..34a44fd
--- /dev/null
+++ b/figs/fig_generator-times.gplot
@@ -0,0 +1,21 @@
+
+set term epslatex size 3.417, 2.3
+set output "fig_generator-times.tex"
+
+set logscale xy
+
+dataPlanarUni = "data/correlation-times/planar-uni.dat"
+dataPlanarPert = "data/correlation-times/planar-pert.dat"
+
+set nokey
+set size ratio 1 / 1.61803398875
+
+set xlabel '$|H|$'
+set ylabel "$\\avg{s_{\\text{\\sc 1c}}}\\tau$"
+
+set format x '$10^{%T}$'
+
+plot dataPlanarUni using (column("H")):((column("L") == 32 ? column("t") : 1/0) * column("S") * exp(-log(column("L")) * (2))):(sqrt((column("dt")/column("t"))**2 + (column("dS")/column("S"))**2) * column("S") * exp(-log(column("L")) * (2))) with yerrorbars pt 0 lw 2 lc rgb "red",\
+ dataPlanarUni using (column("H")):((column("L") == 32 ? column("t") : 1/0) * column("S") * exp(-log(column("L")) * (2))) with lines lc rgb "red",\
+ dataPlanarPert using (column("H")):((column("L") == 32 ? column("t") : 1/0) * column("S") * exp(-log(column("L")) * (2))):(sqrt((column("dt")/column("t"))**2 + (column("dS")/column("S"))**2) * column("t") * column("S") * exp(-log(column("L")) * (2))) with yerrorbars pt 0 lw 2 lc rgb "green",\
+ dataPlanarPert using (column("H")):((column("L") == 32 ? column("t") : 1/0) * column("S") * exp(-log(column("L")) * (2))) with lines lc rgb "green"
diff --git a/figs/fig_harmonic-susceptibilities.gplot b/figs/fig_harmonic-susceptibilities.gplot
new file mode 100644
index 0000000..85d474f
--- /dev/null
+++ b/figs/fig_harmonic-susceptibilities.gplot
@@ -0,0 +1,37 @@
+
+set terminal epslatex size 3.417, 5.3
+set output "fig_harmonic-susceptibilities.tex"
+
+data4 = "data/harmonic-susceptibilities/order-4.dat"
+data6 = "data/harmonic-susceptibilities/order-6.dat"
+
+set palette defined (0 'blue', 0.33 'green', 0.66 'yellow', 1 'red')
+stats data6 using "H"
+set cbrange[STATS_min:STATS_max]
+set logscale xycb
+set nokey
+
+set xrange [1:5000]
+set yrange [0.01:10000]
+
+unset colorbox
+
+set multiplot layout 2,1 margins 0.15, 0.99, 0.225, 0.99 spacing 0,0.015
+set size ratio 1 / 1.61803398875
+
+unset xlabel
+set ylabel '$\chi$' offset 3
+set format x ''
+
+plot data4 using "L":"X":"dX":"H" with yerrorbars pt 0 lw 2 palette,\
+ data4 using "L":"X":"H" with lines palette
+
+set xlabel '$L$'
+set colorbox horizontal user origin 0.15, 0.1 size 0.84, 0.03
+set cblabel '(Top) $h_4$ or (bottom) $h_6$'
+set cbtics format '$10^{%T}$'
+set format x
+
+plot data6 using "L":"X":"dX":"H" with yerrorbars pt 0 lw 2 palette,\
+ data6 using "L":"X":"H" with lines palette
+
diff --git a/makefile b/makefile
index 1803255..d9447e9 100644
--- a/makefile
+++ b/makefile
@@ -1,6 +1,6 @@
DOC=monte-carlo
-FIGS=fig_correlation_collapse-hL fig_correlation fig_metastable fig_correlation-temp fig_clusters_ising2d
+FIGS=fig_correlation_collapse-hL fig_correlation fig_metastable fig_correlation-temp fig_clusters_ising2d fig_correlation-times fig_harmonic-susceptibilities fig_generator-times
DATA=correlation correlation_temp metastable_raw metastable_func
all: ${DOC}.pdf
diff --git a/monte-carlo.tex b/monte-carlo.tex
index d202ef5..370ac0f 100644
--- a/monte-carlo.tex
+++ b/monte-carlo.tex
@@ -534,6 +534,14 @@ conjecture.
\label{fig:cluster_scaling}
\end{figure*}
+\begin{figure}
+ \include{fig_generator-times}
+\end{figure}
+
+\begin{figure}
+ \include{fig_harmonic-susceptibilities}
+\end{figure}
+
We have taken several disparate extensions of cluster methods to spin models
in an external field and generalized them to work for any model of a broad
class. The resulting representation involves the introduction of not a ghost
@@ -552,6 +560,7 @@ perturbations on spin models can be tested numerically
\cite{jose_renormalization_1977, blankschtein_fluctuation-induced_1982,
bruce_coupled_1975, manuel_carmona_$n$-component_2000}.
+<<<<<<< HEAD
\appendix
\section{$\mathrm O(n)$ model at high field}
@@ -620,6 +629,9 @@ whence
\end{align}
\section{Calculating autocorrelation time}
+\begin{figure*}
+ \include{fig_correlation-times}
+\end{figure*}
\begin{acknowledgments}
This work was supported by NSF grant NSF DMR-1719490.
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