From 2d8dabac48abecb6a96376161c4f70846f27de4d Mon Sep 17 00:00:00 2001 From: "kurchan.jorge" Date: Wed, 9 Dec 2020 12:31:36 +0000 Subject: Update on Overleaf. --- bezout.bib | 10 ++++++++++ bezout.tex | 4 ++-- 2 files changed, 12 insertions(+), 2 deletions(-) diff --git a/bezout.bib b/bezout.bib index 37e8f33..a23955b 100644 --- a/bezout.bib +++ b/bezout.bib @@ -194,6 +194,16 @@ year={1992}, publisher={Springer} } +@article{castellani2005spin, + title={Spin-glass theory for pedestrians}, + author={Castellani, Tommaso and Cavagna, Andrea}, + journal={Journal of Statistical Mechanics: Theory and Experiment}, + volume={2005}, + number={05}, + pages={P05012}, + year={2005}, + publisher={IOP Publishing} +} @article{cugliandolo1993analytical, title={Analytical solution of the off-equilibrium dynamics of a long-range spin-glass model}, diff --git a/bezout.tex b/bezout.tex index 753b65b..702f1ae 100644 --- a/bezout.tex +++ b/bezout.tex @@ -39,14 +39,14 @@ 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 family of these are the mean-field spherical p-spin models \cite{crisanti1992sphericalp} +The most tractable family of these are the mean-field spherical p-spin models \cite{crisanti1992sphericalp} (for a review see \cite{castellani2005spin}) defined by the energy: \begin{equation} \label{eq:bare.hamiltonian} H_0 = \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 real Gaussian variables and the $z_i$ are real and constrained to a sphere $\sum_i z_i^2=N$. If there is a single term of a given $p$, this is known as the `pure $p$-spin' model, the case we shall study here. -Also in the algebra \cite{cartwright2013number} and probability literature \cite{auffinger2013complexity,auffinger2013random} +Also in the Algebra \cite{cartwright2013number} and Probability literature \cite{auffinger2013complexity,auffinger2013random}. This problem has been attacked from several angles: the replica trick to compute the Boltzmann--Gibbs distribution\cite{crisanti1992sphericalp}, a Kac--Rice \cite{Kac_1943_On, -- cgit v1.2.3-70-g09d2