Merge branch 'master' of https://git.overleaf.com/5fcce4736e7f601ffb7e1484

1 files changed, 3 insertions, 2 deletions

diff --git a/bezout.tex b/bezout.tex
index fd7f56c..7e932ea 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