From 1b990cf214d7e2ebf003db5f7c36565b36391633 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Wed, 14 Jun 2017 14:10:53 -0400 Subject: changed the way data is processed for the plots --- data/data_square-2048.dat | 500 ++++++++++++++++++++++++++++++++++++++++++++++ essential-ising.tex | 14 +- figs/fig-mag.gplot | 15 +- figs/fig-sus.gplot | 15 +- 4 files changed, 531 insertions(+), 13 deletions(-) create mode 100644 data/data_square-2048.dat diff --git a/data/data_square-2048.dat b/data/data_square-2048.dat new file mode 100644 index 0000000..f51b46f --- /dev/null +++ b/data/data_square-2048.dat @@ -0,0 +1,500 @@ +2048 2.199190000000000 0.000020529700000 -1.547747100244487 0.000050385320576 0.786016052647641 0.000061716852283 3.214943049661604 0.170812224778066 4.823616450215469 0.240884319603407 +2048 2.229190000000000 0.000020529700000 -1.501778846136391 0.000052110597689 0.735348288720776 0.000095075051260 3.872880821586181 0.200235893533496 12.891847530172845 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a/essential-ising.tex b/essential-ising.tex index 1eadf68..4238355 100644 --- a/essential-ising.tex +++ b/essential-ising.tex @@ -185,19 +185,19 @@ explicitly given our scaling ansatz, yielding \def\eqthreedeeone{ \mathcal F^{\text{\textsc{3d}}}(X)&= \frac{AB^{1/3}}{12\pi X^2}e^{-1/(BX)^2} - \bigg[\Gamma(\tfrac16)E_{7/6}((BX)^{-2}) + \bigg[\Gamma(\tfrac16)E_{7/6}(-(BX)^{-2}) } \def\eqthreedeetwo{ - -4BX\Gamma(\tfrac23)E_{5/3}((BX)^{-2})\bigg] + -4BX\Gamma(\tfrac23)E_{5/3}(-(BX)^{-2})\bigg] } \def\eqfourdeeone{ \mathcal F^{\text{\textsc{4d}}}(X)&= - \frac{A}{9\pi X^2}e^{1/(BX)^3} - \Big[3\Gamma(0,(BX)^{-3}) + -\frac{A}{9\pi X^2}e^{1/(BX)^3} + \Big[3\ei(-(BX)^{-3}) } \def\eqfourdeetwo{ - -3\Gamma(\tfrac23)\Gamma(\tfrac13,(BX)^{-3}) - -\Gamma(\tfrac13)\Gamma(-\tfrac13,(BX)^{-3})\Big] + +3\Gamma(\tfrac23)\Gamma(\tfrac13,(BX)^{-3}) + +\Gamma(\tfrac13)\Gamma(-\tfrac13,(BX)^{-3})\Big] } \ifreprint \begin{align} @@ -240,7 +240,7 @@ $C=C_{0-}/T_c$, with $C_{0-}=0.025\,536\,971\,9$ then be extracted by integration and comparison with known exact results at zero field, yielding \[ - \mathcal M^{\text{\textsc{2d}}}(X)=\frac{D}{BX}(BX-1)e^{1/BX}\ei(-1/BX)-D+\mathcal M(0) + \mathcal M^{\text{\textsc{2d}}}(X)=\mathcal M(0)+D-\frac{D}{BX}(BX-1)e^{1/BX}\ei(-1/BX) \label{eq:mag_scaling} \] with $\mathcal M(0)=\big(2(\sqrt2-1)\big)^{1/4}\big((4+3\sqrt2)\sinh^{-1}1\big)^{1/8}$ diff --git a/figs/fig-mag.gplot b/figs/fig-mag.gplot index 73ee9ec..df67fa9 100644 --- a/figs/fig-mag.gplot +++ b/figs/fig-mag.gplot @@ -2,11 +2,20 @@ set terminal pslatex rotate size 3.417,2.111 set multiplot +Tc = 2 / log(1 + sqrt(2)) +Delta = 15. / 8 +beta = 1. / 8 + +t(T) = abs((T - Tc) / T) +h(T, H) = H / T +X(T, H) = h(T, H) * t(T)**(-Delta) + B = 0.0861 A = 0.094 M0 = 1.21039 + func = "figs/fig-mag_data-func.dat" -num = "figs/fig-mag_data-num.dat" +num = "data/data_square-2048.dat" set samples 10000 set key off @@ -16,7 +25,7 @@ set yrange [1.18:1.75] set ylabel offset 1,0 '$Mt^{-\beta}$' set xlabel '$ht^{-\Delta}$' -plot num with yerrorbars pt 0, func using (10**$1 / B):(M0 + 10**($2) * A) with linespoints pt 0 lw 3 +plot num using (X($2, $3)):($6 * t($2)**(-beta)):($7 * t($2)**(-beta)):(hsv2rgb(20 * t($2), 1, 1)) with yerrorbars pt 0 lc rgb variable, func using (10**$1 / B):(M0 + 10**($2) * A) with linespoints pt 0 lw 2 lc rgb "black" set size 0.6,0.6 set origin 0.38,0.2 @@ -27,7 +36,7 @@ set xlabel offset 0,0.5 '\footnotesize$ht^{-\Delta}$' set xtics format '\footnotesize$10^{%g}$' -2,2,3 set ytics format '\footnotesize %g' -plot num using (log10($1)):2:3 with yerrorbars pt 0, func using ($1-log10(B)):(M0 + A * 10**$2) with linespoints pt 0 lw 3 +plot num using (log10(X($2, $3))):($6 * t($2)**(-beta)):($7 * t($2)**(-beta)):(hsv2rgb(20 * t($2), 1, 1)) with yerrorbars pt 0 lc rgb variable, func using ($1-log10(B)):(M0 + A * 10**$2) with linespoints pt 0 lw 2 lc black diff --git a/figs/fig-sus.gplot b/figs/fig-sus.gplot index 5ba371d..c56bafd 100644 --- a/figs/fig-sus.gplot +++ b/figs/fig-sus.gplot @@ -2,10 +2,19 @@ set terminal pslatex rotate size 3.417,2.111 set multiplot +Tc = 2 / log(1 + sqrt(2)) +Delta = 15. / 8 +gamma = 7. / 4 + +t(T) = abs((T - Tc) / T) +h(T, H) = H / T +X(T, H) = h(T, H) * t(T)**(-Delta) + B = 0.173 A = 0.0111 + func = "figs/fig-sus_data-func.dat" -num = "figs/fig-sus_data-num.dat" +num = "data/data_square-2048.dat" set samples 10000 set key off @@ -15,7 +24,7 @@ set yrange [-0.2:13] set ylabel offset 1,0 '$\chi t^{\gamma}\times 10^3$' set xlabel '$ht^{-\Delta}$' -plot num using 1:(10**3 * $2):(10**3 * $3) with yerrorbars pt 0, func using (10**$1 / B):(10**(3+$2) * A) with linespoints pt 0 lw 3 +plot num using (X($2, $3)):(10**3 * $10 * t($2)**gamma):(10**3 * $11 * t($2)**gamma):(hsv2rgb(20 * t($2), 1, 1)) with yerrorbars pt 0 lc rgb variable, func using (10**$1 / B):(10**(3+$2) * A) with linespoints pt 0 lw 2 lc rgb "black" set size 0.6,0.6 set origin 0.38,0.37 @@ -26,7 +35,7 @@ set xlabel offset 0,0.5 '\footnotesize$ht^{-\Delta}$' set xtics format '\footnotesize$10^{%g}$' -2,2,3 set ytics format '\footnotesize$10^{%g}$' -4,1,-2 -plot num using (log10($1)):(log10($2)):($3/$2) with yerrorbars pt 0, func using ($1-log10(B)):($2+log10(A)) with linespoints pt 0 lw 3 +plot num using (log10(X($2, $3))):(log10($10 * t($2)**gamma)):($11 / $10):(hsv2rgb(20 * t($2), 1, 1)) with yerrorbars pt 0 lc rgb variable, func using ($1-log10(B)):($2+log10(A)) with linespoints pt 0 lw 2 lc rgb "black" -- cgit v1.2.3-70-g09d2