The generalized Parisi formula
type: Item
instance of: scholarly article
title: The generalized Parisi formula
zbMATH Open document ID: 1030.60093
DOI: 10.1016/S1631-073X(03)00268-1
author: Michel Talagrand
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2003-09-15T00:00:00Z
review text: This note announces a long awaited and very remarkable result, namely the validity of a certain variational description (first formulated by G. Parisi) of the free energy per site for a whole class of Gaussian mean field spin glasses containing the Sherrington-Kirkpatrick model and the \(p\)-spin interaction models for \(p\) even. The proof is described as building upon Guerra's interpolation scheme as introduced by \textit{F. Guerra} [Commun. Math. Phys. 233, 1-12 (2003; Zbl 1013.82023)], together with some far-reaching refinements of some of the methods developed by \textit{M. Talagrand} [Spin glasses: A challenge for mathematicans. Cavity and mean field models. Berlin: Springer (2003; Zbl 1033.82002)]. To quote the author: ``\dots even though there is quite a distance between Theorem 1.1 and a complete mathematical understanding of the SK model, one can now hope that it is only a matter of time and work until this understanding is reached''.
reviewed by: Michel Sortais
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82D30
Mathematics Subject Classification ID: 82B44
zbMATH DE Number: 1981387
zbMATH Keywords: spin glasses
zbMATH Keywords: Sherrington-Kirkpatrick model
MaRDI profile type: Publication
cites work: Broken replica symmetry bounds in the mean field spin glass model
cites work: Multiple levels of symmetry breaking
cites work: Q4413910
description: scientific article; zbMATH DE number 1981387