From 57ad09701c6b6b8b4362b0dd4fadef48d26e13b4 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Wed, 9 Dec 2020 13:22:33 +0100
Subject: Added new figure, and changed the desert figure to a 3-spin.

---
 bezout.tex         |  12 +++++++++++-
 fig/complexity.pdf | Bin 0 -> 21559 bytes
 fig/desert.pdf     | Bin 22875 -> 22763 bytes
 3 files changed, 11 insertions(+), 1 deletion(-)
 create mode 100644 fig/complexity.pdf

diff --git a/bezout.tex b/bezout.tex
index 7d1335e..968f9e9 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -315,12 +315,22 @@ is the logarithm of the number of configurations of a given $(a,H_0)$.
 This problem may be solved exactly with replicas, {\em but it may also be simulated} \cite{Bray_1980_Metastable}.
 Consider for example the ground-state energy for given $a$, that is, the energy in the limit $\beta_R \rightarrow \infty$ taken adjusting  $\beta_I$ so that $\Im H_0=0$ . For $a=1$ this coincides with the ground-state of the real problem.
 
+\begin{figure}[htpb]
+  \centering
+  \includegraphics{fig/complexity.pdf}
+  \caption{
+    The complexity of the pure 3-spin model at $\epsilon=0$ as a function of
+    $a$ at several values of $\kappa$. The dashed line shows
+    $\frac12\log(p-1)$, while the dotted shows $\log(p-1)$.
+  }
+\end{figure}
+
 \begin{figure}[htpb]
   \centering
   \includegraphics{fig/desert.pdf}
   \caption{
     The minimum value of $a$ for which the complexity is positive as a function
-    of (real) energy $\epsilon$  for the pure 4-spin model at several values of
+    of (real) energy $\epsilon$  for the pure 3-spin model at several values of
     $\kappa$.
   }
 \end{figure}
diff --git a/fig/complexity.pdf b/fig/complexity.pdf
new file mode 100644
index 0000000..66024b1
Binary files /dev/null and b/fig/complexity.pdf differ
diff --git a/fig/desert.pdf b/fig/desert.pdf
index a5af1fa..9ced83f 100644
Binary files a/fig/desert.pdf and b/fig/desert.pdf differ
-- 
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