From fff730e8d72c5b782dfd7fd96aea6e6abed82e86 Mon Sep 17 00:00:00 2001
From: "kurchan.jorge" <kurchan.jorge@gmail.com>
Date: Fri, 1 Jul 2022 14:46:50 +0000
Subject: Update on Overleaf.

---
 frsb_kac-rice.tex | 44 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 44 insertions(+)

(limited to 'frsb_kac-rice.tex')

diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex
index 1c2df68..246a848 100644
--- a/frsb_kac-rice.tex
+++ b/frsb_kac-rice.tex
@@ -721,6 +721,50 @@ E\rangle_2$.
   } \label{fig:2rsb.comparison}
 \end{figure}
 
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+\begin{figure}
+  \begin{center}
+    \includegraphics[width=12cm]{twosys.png}\end{center}
+  \caption{ Weakly coupling two different pure p-spin models we may infer the  phases for the joint model. A sketch of the individual complexities versus energy of each model,
+  the dotted part of the lines corresponds to saddles, and starts at the threshold level.
+  (1) Both systems frozen, lowest energy density.
+(2) One system unfreezes, $1RSB$ Kac-Rice computation. (3) Both systems unfreeze, the gradients are the same in the typical (maximal complexity) values, thus corresponding to the RS Kac-Rice phase.
+The beginning of this phase may start when the system on the right is either
+on the region with minima or with saddles, depending on the whether the gradient of the complexity in the threshold of the system is higher or lower to the one of the ground state of the other.
+(4) and (5) Typical states are saddles, both gradients are the same and hence this is RS. (6) The highest possible energy for minima. Because the gradients at the thresholds of the two systems do not coincide,
+this has subdominant complexity
+  } \label{twosys}
+\end{figure}
+
+
+\begin{figure}
+  \begin{center}
+    \includegraphics[width=12cm]{phase.png}\end{center}
+  \caption{The phase diagram corresponding to two coupled models.
+  } \label{phase}
+\end{figure}
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 \subsection{Full RSB complexity}
 
 
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