From 0d7940769f72b56ad01f2ac8d950b238074a322e Mon Sep 17 00:00:00 2001
From: "kurchan.jorge" <kurchan.jorge@gmail.com>
Date: Mon, 7 Dec 2020 14:53:04 +0000
Subject: Update on Overleaf.

---
 bezout.tex | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

(limited to 'bezout.tex')

diff --git a/bezout.tex b/bezout.tex
index dac5927..ce3e850 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -39,10 +39,11 @@ different topological properties.
 
 Spin-glasses have long been considered the paradigm of `complex landscapes' of many variables, a subject that
 includes Neural Networks and optimization problems, most notably  Constraint Satisfaction ones.
-The most tractable, yet very rich model 
+The most tractable family of these  are the mean-field spherical p-spin models defined by the energy:
 \begin{equation} \label{eq:bare.hamiltonian}
-  H_0 = \frac1{p!}\sum_{i_1\cdots i_p}^NJ_{i_1\cdots i_p}z_{i_1}\cdots z_{i_p},
+  E = \sum_p \frac{c_p}{p!}\sum_{i_1\cdots i_p}^NJ_{i_1\cdots i_p}z_{i_1}\cdots z_{i_p},
 \end{equation}
+where the $J_{i_1\cdots i_p}$ are 
 where $z\in\mathbb C^N$ is constrained by $z^2=N$ and $J$ is a symmetric tensor
 whose elements are complex normal with $\langle|J|^2\rangle=p!/2N^{p-1}$ and
 $\langle J^2\rangle=\kappa\langle|J|^2\rangle$ for complex parameter
-- 
cgit v1.2.3-54-g00ecf

