Computing the number of metastable states in infinite-range models
Disordered Systems and Neural Networks
2007-05-23 v1 Soft Condensed Matter
Abstract
In these notes I will review the results that have been obtained in these last years on the computation of the number of metastable states in infinite-range models of disordered systems. This is a particular case of the problem of computing the exponentially large number of stationary points of a random function. Quite surprisingly supersymmetry plays a crucial role in this problem. A careful analysis of the physical implication of supersymmetry and of supersymmetry breaking will be presented: the most spectacular one is that in the Sherrington-Kirkpatrick model for spin glasses most of the stationary points are saddles, as predicted long time ago.
Keywords
Cite
@article{arxiv.cond-mat/0602349,
title = {Computing the number of metastable states in infinite-range models},
author = {Giorgio Parisi},
journal= {arXiv preprint arXiv:cond-mat/0602349},
year = {2007}
}
Comments
Les houches lectures summer 2005, 22 pages