English

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