From 4d36a1bfb80b211147c458bb1ea1f1ebc29c92e2 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Thu, 28 Oct 2021 15:34:30 +0200
Subject: Improved parametric coordinate plot.

---
 ising_scaling.tex | 69 ++++++++++++++++++++++++++++++++++++++++++++++---------
 1 file changed, 58 insertions(+), 11 deletions(-)

diff --git a/ising_scaling.tex b/ising_scaling.tex
index cba44d8..77d1304 100644
--- a/ising_scaling.tex
+++ b/ising_scaling.tex
@@ -359,24 +359,71 @@ entirely fixed, and it will be truncated at finite order.
 
     set xlabel '$u_t$'
     set ylabel '$u_h$'
-    set key left bottom reverse title '\raisebox{1em}{$R$}' 
+    unset key
 
-    set xzeroaxis
-    set yzeroaxis
+    set xrange [-4.5:4.5]
+    set yrange [-3.5:3.5]
 
     set parametric
+    set style data lines
     set trange [-t0:t0]
 
-    plot \
-      f(t),g(t) title '$1$', \
-      2*f(t),2**del*g(t) title '$2$', \
-      4*f(t),4**del*g(t) title '$4$', \
-      t*f(t0/4),t**del*g(t0/4)
+    plot sample \
+      [-t0:t0:0.001] '+' u (0.5*f($1)):(0.5*g($1)) lc black , \
+      [-t0:t0:0.001] '+' u (f($1)):(g($1)) lc black , \
+      [-t0:t0:0.001] '+' u (1.5*f($1)):(1.5**del*g($1)) lc black , \
+      [-t0:t0:0.001] '+' u (2*f($1)):(2**del*g($1)) lc black , \
+      [-t0:t0:0.001] '+' u (2.5*f($1)):(2.5**del*g($1)) lc black , \
+      [-t0:t0:0.001] '+' u (3*f($1)):(3**del*g($1)) lc black , \
+      [-t0:t0:0.001] '+' u (3.5*f($1)):(3.5**del*g($1)) lc black , \
+      [-t0:t0:0.001] '+' u (4*f($1)):(4**del*g($1)) lc black , \
+      [-t0:t0:0.001] '+' u (4.5*f($1)):(4.5**del*g($1)) lc black , \
+      [-t0:t0:0.001] '+' u (5*f($1)):(5**del*g($1)) lc black , \
+      [-t0:t0:0.001] '+' u (5.5*f($1)):(5.5**del*g($1)) lc black , \
+      [-t0:t0:0.001] '+' u (6*f($1)):(6**del*g($1)) lc black , \
+      [-t0:t0:0.001] '+' u (6.5*f($1)):(6.5**del*g($1)) lc black , \
+      [-t0:t0:0.001] '+' u (7*f($1)):(7**del*g($1)) lc black , \
+      [-t0:t0:0.001] '+' u (7.5*f($1)):(7.5**del*g($1)) lc black , \
+      [-t0:t0:0.001] '+' u (8*f($1)):(8**del*g($1)) lc black , \
+      [-t0:t0:0.001] '+' u (8.5*f($1)):(8.5**del*g($1)) lc black , \
+      [0:20:0.1] '+' u ($1*f(0)):($1**del*g(0)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(t0/16)):($1**del*g(t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(2*t0/16)):($1**del*g(2*t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(3*t0/16)):($1**del*g(3*t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(4*t0/16)):($1**del*g(4*t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(5*t0/16)):($1**del*g(5*t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(6*t0/16)):($1**del*g(6*t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(7*t0/16)):($1**del*g(7*t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(8*t0/16)):($1**del*g(8*t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(9*t0/16)):($1**del*g(9*t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(10*t0/16)):($1**del*g(10*t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(11*t0/16)):($1**del*g(11*t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(12*t0/16)):($1**del*g(12*t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(13*t0/16)):($1**del*g(13*t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(14*t0/16)):($1**del*g(14*t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(15*t0/16)):($1**del*g(15*t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(16*t0/16)):($1**del*g(16*t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(-t0/16)):($1**del*g(-t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(2*-t0/16)):($1**del*g(2*-t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(3*-t0/16)):($1**del*g(3*-t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(4*-t0/16)):($1**del*g(4*-t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(5*-t0/16)):($1**del*g(5*-t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(6*-t0/16)):($1**del*g(6*-t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(7*-t0/16)):($1**del*g(7*-t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(8*-t0/16)):($1**del*g(8*-t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(9*-t0/16)):($1**del*g(9*-t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(10*-t0/16)):($1**del*g(10*-t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(11*-t0/16)):($1**del*g(11*-t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(12*-t0/16)):($1**del*g(12*-t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(13*-t0/16)):($1**del*g(13*-t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(14*-t0/16)):($1**del*g(14*-t0/16)) dt 2 lc black , \
+      [0:20:0.1] '+' u ($1*f(15*-t0/16)):($1**del*g(15*-t0/16)) dt 2 lc black , \
   \end{gnuplot}
   \caption{
-    Example of the parametric coordinates. Lines are of constant $R$ from
-    $-\theta_0$ to $\theta_0$ for $g(\theta)$ taken from the $n=6$ entry of
-    Table \ref{tab:fits}. {\color{blue} \bf XXX Can we have lines of constant $\theta$ as well? Maybe dashed? Also maybe smaller radii, $R=1/4$, 1/2, and 1?}
+    Example of the parametric coordinates. Solid lines are of constant
+    $R=\frac12,1,\ldots,8\frac12$  and dashed lines are of constant
+    $\theta=\pm0\theta_0,\frac1{16}\theta_0,\ldots,\theta_0$ for $g(\theta)$ taken
+    from the $n=6$ entry of Table \ref{tab:fits}.
   } \label{fig:schofield}
 \end{figure}
 
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