From 5cfe467fbefdc1236b7aa01bc94c19e2ac87c306 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Thu, 25 May 2023 14:51:00 +0200
Subject: No gnuplot for APS.

---
 ising_scaling.tex | 280 ++++--------------------------------------------------
 1 file changed, 16 insertions(+), 264 deletions(-)

(limited to 'ising_scaling.tex')

diff --git a/ising_scaling.tex b/ising_scaling.tex
index 53f76ad..8c41c07 100644
--- a/ising_scaling.tex
+++ b/ising_scaling.tex
@@ -20,7 +20,6 @@ linkcolor=purple
 \usepackage{graphicx}
 \usepackage{xcolor}
 \usepackage{tikz-cd}
-\usepackage[subfolder]{gnuplottex} % need to compile separately for APS
 \usepackage{setspace}
 \usepackage{tabularx}
 
@@ -355,81 +354,8 @@ In practice the infinite series in \eqref{eq:schofield.funcs} cannot be
 entirely fixed, and it will be truncated at finite order.
 
 \begin{figure}
-  \begin{gnuplot}[terminal=epslatex]
-    t0 = 1.36261
-    g0 = 0.438453
-    g1 = -0.0531270
-    g2 = -0.00391478
-    g3 = -0.000408016
-    g4 = 0.0000262629
-    g5 = -0.00000109745
-
-    f(t) = 1-t**2
-    g(t) = (1-(t/t0)**2)*(g0*t + g1*t**3 + g2*t**5 + g3*t**7 + g4*t**9 + g5*t**11)
-    del = 15.0/8.0
-
-    set xlabel '$u_t$'
-    set ylabel '$u_h$'
-    unset key
-
-    set xrange [-4.5:4.5]
-    set yrange [-3.5:3.5]
-
-    set parametric
-    set style data lines
-    set trange [-t0:t0]
-
-    plot sample \
-      [-t0:t0:0.001] '+' u (0.5*f($1)):(0.5*g($1)) lc black  lw 2 , \
-      [-t0:t0:0.001] '+' u (f($1)):(g($1)) lc black  lw 2 , \
-      [-t0:t0:0.001] '+' u (1.5*f($1)):(1.5**del*g($1)) lc black  lw 2 , \
-      [-t0:t0:0.001] '+' u (2*f($1)):(2**del*g($1)) lc black  lw 2 , \
-      [-t0:t0:0.001] '+' u (2.5*f($1)):(2.5**del*g($1)) lc black  lw 2 , \
-      [-t0:t0:0.001] '+' u (3*f($1)):(3**del*g($1)) lc black  lw 2 , \
-      [-t0:t0:0.001] '+' u (3.5*f($1)):(3.5**del*g($1)) lc black  lw 2 , \
-      [-t0:t0:0.001] '+' u (4*f($1)):(4**del*g($1)) lc black  lw 2 , \
-      [-t0:t0:0.001] '+' u (4.5*f($1)):(4.5**del*g($1)) lc black  lw 2 , \
-      [-t0:t0:0.001] '+' u (5*f($1)):(5**del*g($1)) lc black  lw 2 , \
-      [-t0:t0:0.001] '+' u (5.5*f($1)):(5.5**del*g($1)) lc black  lw 2 , \
-      [-t0:t0:0.001] '+' u (6*f($1)):(6**del*g($1)) lc black  lw 2 , \
-      [-t0:t0:0.001] '+' u (6.5*f($1)):(6.5**del*g($1)) lc black  lw 2 , \
-      [-t0:t0:0.001] '+' u (7*f($1)):(7**del*g($1)) lc black  lw 2 , \
-      [-t0:t0:0.001] '+' u (7.5*f($1)):(7.5**del*g($1)) lc black  lw 2 , \
-      [-t0:t0:0.001] '+' u (8*f($1)):(8**del*g($1)) lc black  lw 2 , \
-      [-t0:t0:0.001] '+' u (8.5*f($1)):(8.5**del*g($1)) lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(0)):($1**del*g(0)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(t0/16)):($1**del*g(t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(2*t0/16)):($1**del*g(2*t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(3*t0/16)):($1**del*g(3*t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(4*t0/16)):($1**del*g(4*t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(5*t0/16)):($1**del*g(5*t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(6*t0/16)):($1**del*g(6*t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(7*t0/16)):($1**del*g(7*t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(8*t0/16)):($1**del*g(8*t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(9*t0/16)):($1**del*g(9*t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(10*t0/16)):($1**del*g(10*t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(11*t0/16)):($1**del*g(11*t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(12*t0/16)):($1**del*g(12*t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(13*t0/16)):($1**del*g(13*t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(14*t0/16)):($1**del*g(14*t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(15*t0/16)):($1**del*g(15*t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(16*t0/16)):($1**del*g(16*t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(-t0/16)):($1**del*g(-t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(2*-t0/16)):($1**del*g(2*-t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(3*-t0/16)):($1**del*g(3*-t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(4*-t0/16)):($1**del*g(4*-t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(5*-t0/16)):($1**del*g(5*-t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(6*-t0/16)):($1**del*g(6*-t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(7*-t0/16)):($1**del*g(7*-t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(8*-t0/16)):($1**del*g(8*-t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(9*-t0/16)):($1**del*g(9*-t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(10*-t0/16)):($1**del*g(10*-t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(11*-t0/16)):($1**del*g(11*-t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(12*-t0/16)):($1**del*g(12*-t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(13*-t0/16)):($1**del*g(13*-t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(14*-t0/16)):($1**del*g(14*-t0/16)) dt 2 lc black  lw 2 , \
-      [0:20:0.1] '+' u ($1*f(15*-t0/16)):($1**del*g(15*-t0/16)) dt 2 lc black  lw 2
-  \end{gnuplot}
+  \centering
+  \includegraphics{ising_scaling-gnuplottex-fig1.pdf}
   \caption{
     Example of the parametric coordinates. Solid lines are of constant
     $R=\frac12,1,\ldots,8\frac12$  and dashed lines are of constant
@@ -914,34 +840,8 @@ values of both are plotted.
 \end{table}
 
 \begin{figure}
-  \begin{gnuplot}[terminal=epslatex]
-    set linetype 1 lc rgb "#5e81b5" lw 2 ps 2
-    set linetype 2 lc rgb "#e19c24" lw 2 ps 2
-    set linetype 3 lc rgb "#8fb032" lw 2 ps 2
-    set linetype 4 lc rgb "#eb6235" lw 2 ps 2
-    set linetype 5 lc rgb "#8778b3" lw 2 ps 2
-    set linetype 6 lc rgb "#c56e1a" lw 2 ps 2
-
-    dat = 'data/phi_comparison.dat'
-
-    set xlabel '$n$'
-    set xrange [1.5:6.5]
-
-    set logscale y
-    set format y '$10^{%T}$'
-    set ylabel '$|\Delta\mathcal F_0^{(m)}|$'
-    set yrange [0.000000005:0.0005]
-
-    set style data yerrorlines
-    set key title '\raisebox{0.5em}{$m$}' bottom left
-
-    plot \
-      dat using 1:2:3 title '0', \
-      dat using 1:4:5 title '1', \
-      dat using 1:6:7 title '2', \
-      dat using 1:8:9 title '3', \
-      dat using 1:10:11 title '4'
-  \end{gnuplot}
+  \centering
+  \includegraphics{ising_scaling-gnuplottex-fig2.pdf}
   \caption{
     The error in the $m$th derivative of the scaling function $\mathcal F_0$
     with respect to $\eta$ evaluated at $\eta=0$, as a function of the
@@ -955,29 +855,8 @@ values of both are plotted.
 
 
 \begin{figure}
-  \begin{gnuplot}[terminal=epslatex]
-    set linetype 1 lc rgb "#5e81b5" lw 2 ps 2
-    set linetype 2 lc rgb "#e19c24" lw 2 ps 2
-    set linetype 3 lc rgb "#8fb032" lw 2 ps 2
-    set linetype 4 lc rgb "#eb6235" lw 2 ps 2
-    set linetype 5 lc rgb "#8778b3" lw 2 ps 2
-    set linetype 6 lc rgb "#c56e1a" lw 2 ps 2
-
-    dat1 = 'data/phi_numeric.dat'
-    dat2 = 'data/phi_series_ours_2.dat'
-    dat3 = 'data/phi_series_ours_6.dat'
-    set key top right
-    set logscale y
-    set xlabel '$m$'
-    set ylabel '$|\mathcal F_0^{(m)}|$'
-    set format y '$10^{%T}$'
-    set xrange [-0.5:10.5]
-
-    plot \
-      dat1 using 1:(abs($2)):3 title 'Numeric' with yerrorbars, \
-      dat2 using 1:(abs($2)) title 'This work ($n=2$)', \
-      dat3 using 1:(abs($2)) title 'This work ($n=6$)'
-  \end{gnuplot}
+  \centering
+  \includegraphics{ising_scaling-gnuplottex-fig3.pdf}
   \caption{
     The series coefficients for the scaling function $\mathcal F_0$ as a
     function of polynomial order $m$. The numeric values are from Table
@@ -995,33 +874,8 @@ $\mathcal F_+$ in Fig.~\ref{fig:ghigh.series}, and for $\mathcal F_0$ in
 Fig.~\ref{fig:phi.series}.
 
 \begin{figure}
-  \begin{gnuplot}[terminal=epslatex]
-    set linetype 1 lc rgb "#5e81b5" lw 2 ps 2
-    set linetype 2 lc rgb "#e19c24" lw 2 ps 2
-    set linetype 3 lc rgb "#8fb032" lw 2 ps 2
-    set linetype 4 lc rgb "#eb6235" lw 2 ps 2
-    set linetype 5 lc rgb "#8778b3" lw 2 ps 2
-    set linetype 6 lc rgb "#c56e1a" lw 2 ps 2
-
-    dat1 = 'data/glow_numeric.dat'
-    dat2 = 'data/glow_series_ours_0.dat'
-    dat3 = 'data/glow_series_ours_6.dat'
-    dat4 = 'data/glow_series_caselle.dat'
-
-    set xlabel '$m$'
-    set xrange [0:14.5]
-
-    set key top left Left reverse
-    set logscale y
-    set ylabel '$\mathcal F_-^{(m)}$'
-    set format y '$10^{%T}$'
-
-    plot \
-      dat1 using 1:(abs($2)):3 title 'Numeric' with yerrorbars, \
-      dat2 using 1:(abs($2)) title 'This work ($n=2$)', \
-      dat3 using 1:(abs($2)) title 'This work ($n=6$)', \
-      dat4 using 1:(abs($2)) title 'Caselle \textit{et al.}'
-  \end{gnuplot}
+  \centering
+  \includegraphics{ising_scaling-gnuplottex-fig4.pdf}
   \caption{
     The series coefficients for the scaling function $\mathcal F_-$ as a
     function of polynomial order $m$. The numeric values are from Table
@@ -1031,32 +885,8 @@ Fig.~\ref{fig:phi.series}.
 \end{figure}
 
 \begin{figure}
-  \begin{gnuplot}[terminal=epslatex]
-    set linetype 1 lc rgb "#5e81b5" lw 2 ps 2
-    set linetype 2 lc rgb "#e19c24" lw 2 ps 2
-    set linetype 3 lc rgb "#8fb032" lw 2 ps 2
-    set linetype 4 lc rgb "#eb6235" lw 2 ps 2
-    set linetype 5 lc rgb "#8778b3" lw 2 ps 2
-    set linetype 6 lc rgb "#c56e1a" lw 2 ps 2
-
-    dat1 = 'data/ghigh_numeric.dat'
-    dat2 = 'data/ghigh_series_ours_2.dat'
-    dat3 = 'data/ghigh_series_ours_6.dat'
-    dat4 = 'data/ghigh_caselle.dat'
-
-    set key top left Left reverse
-    set logscale y
-    set xlabel '$m$'
-    set ylabel '$\mathcal F_+^{(m)}$'
-    set format y '$10^{%T}$'
-    set xrange [1.5:14.5]
-
-    plot \
-      dat1 using 1:(abs($2)):3 title 'Numeric' with yerrorbars, \
-      dat2 using 1:(abs($2)) title 'This work ($n=2$)', \
-      dat3 using 1:(abs($2)) title 'This work ($n=6$)', \
-      dat4 using 1:(abs($2)) title 'Caselle \textit{et al.}'
-  \end{gnuplot}
+  \centering
+  \includegraphics{ising_scaling-gnuplottex-fig5.pdf}
   \caption{
     The series coefficients for the scaling function $\mathcal F_+$ as a
     function of polynomial order $m$. The numeric values are from Table
@@ -1081,34 +911,8 @@ would converge better.
 Notice that this infelicity does not appear to cause significant errors in the function $\mathcal F_-(\theta)$ or its low order derivatives, as evidenced by the convergence in Fig.~\ref{fig:error}.
 
 \begin{figure}
-  \begin{gnuplot}[terminal=epslatex]
-    set linetype 1 lc rgb "#5e81b5" lw 2 ps 2
-    set linetype 2 lc rgb "#e19c24" lw 2 ps 2
-    set linetype 3 lc rgb "#8fb032" lw 2 ps 2
-    set linetype 4 lc rgb "#eb6235" lw 2 ps 2
-    set linetype 5 lc rgb "#8778b3" lw 2 ps 2
-    set linetype 6 lc rgb "#c56e1a" lw 2 ps 2
-
-    dat1 = 'data/glow_numeric.dat'
-    dat2 = 'data/glow_series_ours_0.dat'
-    dat3 = 'data/glow_series_ours_6.dat'
-    dat4 = 'data/glow_series_caselle.dat'
-
-    set xlabel '$m$'
-    set xrange [0:14.5]
-
-    set key top left Left reverse
-    set ylabel '$\mathcal F_-^{(m)}/\mathcal F_-^\infty(m)$'
-
-    os = 1.3578383417065954956
-    asmp(n) = os / (2 * pi) * (2 * os / pi)**(n-1) * gamma(n - 1) / pi
-
-    plot \
-      dat1 using 1:(abs($2) / asmp($1)):($3 / asmp($1)) title 'Numeric' with yerrorbars, \
-      dat2 using 1:(abs($2) / asmp($1)) title 'This work ($n=2$)', \
-      dat3 using 1:(abs($2) / asmp($1)) title 'This work ($n=6$)', \
-      dat4 using 1:(abs($2) / asmp($1)) title 'Caselle \textit{et al.}'
-  \end{gnuplot}
+  \centering
+  \includegraphics{ising_scaling-gnuplottex-fig6.pdf}
   \caption{
     The series coefficients for the scaling function $\mathcal F_-$ as a
     function of polynomial order $m$, rescaled by their asymptotic limit
@@ -1119,35 +923,8 @@ Notice that this infelicity does not appear to cause significant errors in the f
 \end{figure}
 
 \begin{figure}
-  \begin{gnuplot}[terminal=epslatex]
-    set linetype 1 lc rgb "#5e81b5" lw 2 ps 2
-    set linetype 2 lc rgb "#e19c24" lw 2 ps 2
-    set linetype 3 lc rgb "#8fb032" lw 2 ps 2
-    set linetype 4 lc rgb "#eb6235" lw 2 ps 2
-    set linetype 5 lc rgb "#8778b3" lw 2 ps 2
-    set linetype 6 lc rgb "#c56e1a" lw 2 ps 2
-
-    dat1 = 'data/ghigh_numeric.dat'
-    dat2 = 'data/ghigh_series_ours_2.dat'
-    dat3 = 'data/ghigh_series_ours_6.dat'
-    dat4 = 'data/ghigh_caselle.dat'
-
-    set xlabel '$m$'
-    set ylabel '$\mathcal F_+^{(m)}/\mathcal F_+^\infty(m)$'
-    set yrange [0.8:1.5]
-    set xrange [1.5:14.5]
-
-    xYL = 0.18930
-    AYL = 1.37
-    sigma = 0.833333333333
-    asmp(n) = -AYL * 2 * exp(log(xYL)*(sigma-n))*gamma(sigma+1)/gamma(n+1)/gamma(sigma-n+1)
-
-    plot \
-    dat1 using 1:(abs($2) / abs(asmp($1))):($3 / asmp($1)) title 'Numeric' with yerrorbars, \
-      dat2 using 1:(abs($2) / asmp($1)) title 'This work ($n=2$)', \
-      dat3 using 1:(abs($2) / asmp($1)) title 'This work ($n=6$)', \
-      dat4 using 1:(abs($2) / asmp($1)) title 'Caselle \textit{et al.}'
-  \end{gnuplot}
+  \centering
+  \includegraphics{ising_scaling-gnuplottex-fig7.pdf}
   \caption{
     The series coefficients for the scaling function $\mathcal F_+$ as a
     function of polynomial order $m$, rescaled by their asymptotic limit
@@ -1168,33 +945,8 @@ and the approximate functions defined here show the appropriate divergence in
 the ratio.
 
 \begin{figure}
-  \begin{gnuplot}[terminal=epslatex]
-    set linetype 1 lc rgb "#5e81b5" lw 2 ps 2
-    set linetype 2 lc rgb "#e19c24" lw 2 ps 2
-    set linetype 3 lc rgb "#8fb032" lw 2 ps 2
-    set linetype 4 lc rgb "#eb6235" lw 2 ps 2
-    set linetype 5 lc rgb "#8778b3" lw 2 ps 2
-    set linetype 6 lc rgb "#c56e1a" lw 2 ps 2
-
-    dat1 = 'data/glow_numeric.dat'
-    dat2 = 'data/glow_series_ours_0.dat'
-    dat3 = 'data/glow_series_ours_6.dat'
-    dat4 = 'data/glow_series_caselle.dat'
-    ratLast(x) = (back2 = back1, back1 = x, back1 / back2)
-    back1 = 0
-    back2 = 0
-
-    set xlabel '$1/m$'
-    set xrange [0:0.55]
-    set ylabel '$\mathcal F_-^{(m)}/\mathcal F_-^{(m-1)}$'
-    set yrange [0:15]
-
-    plot \
-      dat1 using (1/$1):(abs(ratLast($2))) title 'Numeric', \
-      dat2 using (1/$1):(abs(ratLast($2))) title 'This work ($n=2$)', \
-      dat3 using (1/$1):(abs(ratLast($2))) title 'This work ($n=6$)', \
-      dat4 using (1/$1):(abs(ratLast($2))) title 'Caselle \textit{et al.}'
-  \end{gnuplot}
+  \centering
+  \includegraphics{ising_scaling-gnuplottex-fig8.pdf}
   \caption{
     Sequential ratios of the series coefficients of the scaling function
     $\mathcal F_-$ as a function of inverse polynomial order $m$. The
-- 
cgit v1.2.3-70-g09d2

