From 08047f31e51e25c764622630d22b01dd404d80ec Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Wed, 16 Jun 2021 17:56:03 +0200
Subject: Added plot of ground state.

---
 stokes.tex | 35 +++++++++++++++++++++++++++++++++++
 1 file changed, 35 insertions(+)

(limited to 'stokes.tex')

diff --git a/stokes.tex b/stokes.tex
index fc73b03..af66e3a 100644
--- a/stokes.tex
+++ b/stokes.tex
@@ -372,6 +372,41 @@ imaginary energy join.
   H_p=\frac1{p!}\sum_{i_1\cdots i_p}J_{i_1\cdots i_p}z_{i_1}\cdots z_{i_p}
 \end{equation}
 
+\begin{figure}
+  \begin{gnuplot}[terminal=epslatex, terminaloptions={size 8.65cm,5.35cm}]
+    set parametric
+    set hidden3d
+    set isosamples 100,25
+    set samples 100,100
+    unset key
+    set dummy u,r
+    set urange [-pi:pi]
+    set vrange [1:1.5]
+    set cbrange [0:2]
+    set xyplane 0
+
+    set xlabel '$\operatorname{Re}\epsilon$'
+    set ylabel '$\operatorname{Im}\epsilon$'
+    set zlabel '$r$'
+    set cblabel '$\frac\epsilon{\epsilon_{\mathrm{th}}}$'
+
+    p = 4
+    set palette defined (0 "blue", 0.99 "blue", 1.0 "white", 1.01 "red", 2 "red")
+    set pm3d depthorder border linewidth 0.5
+
+    s(r) = sqrt(0.75 * log(9 * r**4 / (1 + r**2 + r**4)) / (8 * r**4 - r**2 - 1))
+    x(u, r) = cos(u) * s(r) * sqrt(1 + 5 * r**2 + 5 * r**4 + r**6)
+    y(u, r) = sin(u) * s(r) * sqrt((r**2 - 1)**3)
+    thres(u, r) = ((x(u,r) / (r**(p - 2) + 1))**2 + (y(u,r) / (r**(p - 2) - 1))**2) / ((p - 1) / (2 * p * r**(p - 2)))
+
+    splot "++" using (x(u, r)):(y(u, r)):2:(thres(u, r)) with pm3d lc palette
+  \end{gnuplot}
+  \caption{
+    The surface of extant states for the 4-spin model, that is, those for which
+    the complexity is zero.
+  }
+\end{figure}
+
 \subsection{(2 + 4)-spin}
 
 \begin{equation}
-- 
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