From 240f82255f0570d07139daab702459ab0ea2fce9 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Fri, 21 Sep 2018 11:30:43 -0400 Subject: started new figs --- data/correlation-times/heisenberg-pert.dat | 93 ++++++++++++++++++++ data/correlation-times/heisenberg.dat | 93 ++++++++++++++++++++ data/correlation-times/ising-2d.dat | 137 +++++++++++++++++++++++++++++ data/correlation-times/ising-3d.dat | 111 +++++++++++++++++++++++ data/correlation-times/planar-pert.dat | 107 ++++++++++++++++++++++ data/correlation-times/planar-uni.dat | 46 ++++++++++ data/correlation-times/planar.dat | 107 ++++++++++++++++++++++ data/correlation-times/potts-3.dat | 120 +++++++++++++++++++++++++ data/correlation-times/potts-4.dat | 120 +++++++++++++++++++++++++ 9 files changed, 934 insertions(+) create mode 100644 data/correlation-times/heisenberg-pert.dat create mode 100644 data/correlation-times/heisenberg.dat create mode 100644 data/correlation-times/ising-2d.dat create mode 100644 data/correlation-times/ising-3d.dat create mode 100644 data/correlation-times/planar-pert.dat create mode 100644 data/correlation-times/planar-uni.dat create mode 100644 data/correlation-times/planar.dat create mode 100644 data/correlation-times/potts-3.dat create mode 100644 data/correlation-times/potts-4.dat (limited to 'data') diff --git a/data/correlation-times/heisenberg-pert.dat b/data/correlation-times/heisenberg-pert.dat new file mode 100644 index 0000000..17b2099 --- /dev/null +++ b/data/correlation-times/heisenberg-pert.dat @@ -0,0 +1,93 @@ +L T H S dS t dt + +4 1.44325 0.000000316228 9.56983472472473 0.00219465797457129 18.21184038321221 0.04410825728820503 +4 1.44325 0.000001 9.56793718718719 0.00219482540003218 18.16277042570554 0.0439894120608539 +4 1.44325 0.00000316228 9.57084031031031 0.002194285199316918 18.20319824817915 0.04408732642632965 +4 1.44325 0.00001 9.57084600600601 0.002195643760292323 18.21156821151843 0.04410759810061919 +4 1.44325 0.0000316228 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v1.2.3-70-g09d2 From 1676b1bfc1544ba7049f198cb4ae75bea0513014 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Mon, 24 Sep 2018 15:27:05 -0400 Subject: many figure changes --- "\\" | 37 +++++ data/correlation-times/heisenberg-pert.dat | 36 +++-- data/correlation-times/ising-2d.dat | 226 ++++++++++++++-------------- data/correlation-times/ising-3d.dat | 198 ++++++++++++------------ data/correlation-times/planar-pert.dat | 44 +++--- data/harmonic-susceptibilities/order-4.dat | 232 ++++++++++++++++++++++++++++ data/harmonic-susceptibilities/order-6.dat | 233 +++++++++++++++++++++++++++++ figs/fig_correlation-times.gplot | 122 +++++++++++++-- figs/fig_generator-times.gplot | 21 +++ figs/fig_harmonic-susceptibilities.gplot | 37 +++++ makefile | 2 +- monte-carlo.pdf | Bin 196937 -> 0 bytes monte-carlo.tex | 12 ++ test.pdf | Bin 13365 -> 0 bytes 14 files changed, 942 insertions(+), 258 deletions(-) create mode 100644 "\\" create mode 100644 data/harmonic-susceptibilities/order-4.dat create mode 100644 data/harmonic-susceptibilities/order-6.dat create mode 100644 figs/fig_generator-times.gplot create mode 100644 figs/fig_harmonic-susceptibilities.gplot delete mode 100644 monte-carlo.pdf delete mode 100644 test.pdf (limited to 'data') diff --git "a/\\" "b/\\" new file mode 100644 index 0000000..51bc3b4 --- /dev/null +++ "b/\\" @@ -0,0 +1,37 @@ + +set term pdf size 3.417, 5.3 +set output "test.pdf" + +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/data/correlation-times/heisenberg-pert.dat b/data/correlation-times/heisenberg-pert.dat index 17b2099..c708670 100644 --- a/data/correlation-times/heisenberg-pert.dat +++ b/data/correlation-times/heisenberg-pert.dat @@ -53,7 +53,10 @@ L T H S dS t dt 16 1.44325 0.00316228 156.9158591591592 0.060315107773364 86.2338452865457 0.4534264446128828 16 1.44325 0.01 198.1013277577578 0.07027959116611155 65.05316249687783 0.2972643455003248 16 1.44325 0.0316228 281.6223049149149 0.0891949692960346 43.7198250391909 0.1637833228973357 -16 1.44325 0.1 425.0650075426914 0.1278546237882936 28.24290325091006 0.0923258096218324 +16 1.44325 0.1 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0.1731812233148764 +316.22800000000001 0.7 64 4.66939034645033 0.4614023867054954 +316.22800000000001 0.7 128 16.90727812528816 1.117891907701382 +316.22800000000001 0.7 256 35.46182023067169 4.353367342543534 +316.22800000000001 0.7 512 222.2336840360783 29.05753041952091 +316.22800000000001 0.7 1024 818.273273412072 65.02231883637881 + +1000.00000000000000 0.7 4 0.07158025674716129 0.003149452151801607 +1000.00000000000000 0.7 8 0.1885205107451985 0.01136295780992405 +1000.00000000000000 0.7 16 0.5488744374698383 0.04112638091641204 +1000.00000000000000 0.7 32 1.417128308926294 0.1549457657372247 +1000.00000000000000 0.7 64 3.998505686350395 0.398718532188834 +1000.00000000000000 0.7 128 16.32145164329424 1.285463668329433 +1000.00000000000000 0.7 256 73.67021605001355 6.023050054334635 +1000.00000000000000 0.7 512 133.8234861054142 28.37881453817464 + +3162.28000000000020 0.7 4 0.07421083425266975 0.004824419725028251 +3162.28000000000020 0.7 8 0.192965627401845 0.01486017393015611 +3162.28000000000020 0.7 16 0.5283902981831342 0.05780746509625447 +3162.28000000000020 0.7 32 1.55599088859617 0.1664276584383926 +3162.28000000000020 0.7 64 4.812066689362707 0.5935963582738736 +3162.28000000000020 0.7 128 17.04980112978124 0.994769023786145 +3162.28000000000020 0.7 256 57.72767184425902 3.750560819887596 +3162.28000000000020 0.7 512 158.0718280519276 34.94555443829426 +3162.28000000000020 0.7 1024 318.4511854307493 80.3180879754106 \ No newline at end of file diff --git a/figs/fig_correlation-times.gplot b/figs/fig_correlation-times.gplot index fec61d4..7dac658 100644 --- a/figs/fig_correlation-times.gplot +++ b/figs/fig_correlation-times.gplot @@ -1,11 +1,55 @@ -#set terminal epslatex size 6.834, 2.81576 -#set output "fig_clusters_ising2d.tex" +# data and constants, sorted by column -set term pdf -set output "test.pdf" +isingRange = "[0.0000005:5000000]" -set key autotitle columnhead +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" @@ -17,25 +61,73 @@ 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 format x '$10^{%T}$' set logscale xy -set ylabel '$\avg{s_{\text{\sc 1c}}}L^{-\gamma/\nu}$' -set xlabel '$hL^{\beta\delta/\nu}$' +scaledylabel = '"$\\avg{s_{\\text{\\sc 1c}}}L^{-\\gamma/\\nu}$" offset 2,0' -data3Potts2D = "data/correlation-times/potts-3.dat" - +# 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 -beta3Potts2D = 1.0 / 9.0 -nu3Potts2D = 5.0 / 6.0 -delta3Potts2D = 14.0 -gamma3Potts2D = 13.0 / 9.0 -z3Potts2D = 0.55 +# 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: ${DOC}.pdf diff --git a/monte-carlo.pdf b/monte-carlo.pdf deleted file mode 100644 index 27aa7ac..0000000 Binary files a/monte-carlo.pdf and /dev/null differ diff --git a/monte-carlo.tex b/monte-carlo.tex index 7aca41a..010b588 100644 --- a/monte-carlo.tex +++ b/monte-carlo.tex @@ -545,6 +545,14 @@ conjecture. \label{fig:cluster_scaling} \end{figure*} +\begin{figure} + \include{fig_generator-times} +\end{figure} + +\begin{figure} + \include{fig_harmonic-susceptibilities} +\end{figure} + We have taken several disparate extensions of cluster methods to spin models in an external field and generalized them to work for any model of a broad class. The resulting representation involves the introduction of not a ghost @@ -563,6 +571,10 @@ perturbations on spin models can be tested numerically \cite{jose_renormalization_1977, blankschtein_fluctuation-induced_1982, bruce_coupled_1975, manuel_carmona_$n$-component_2000}. +\begin{figure*} + \include{fig_correlation-times} +\end{figure*} + \begin{acknowledgments} This work was supported by NSF grant NSF DMR-1719490. \end{acknowledgments} diff --git a/test.pdf b/test.pdf deleted file mode 100644 index a368751..0000000 Binary files a/test.pdf and /dev/null differ -- cgit v1.2.3-70-g09d2