Mean field models for spin glasses

by Talagrand, Michel

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Title Statements

Full title :Mean field models for spin glasses. / Michel Talagrand.

Summary

This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians" in two volumes (this is the 2nd volume). In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, of considerable interest for several branches of science (statistical physics, neural networks and computer science). The physicists studied them by non-rigorous methods and predicted spectacular behaviors. This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics. The present Volume II contains a considerable amount of new material, in particular all the fundamental low-temperature results obtained after the publication of the first edition

Edition Statements

Publication Date:©2011

Publication Statements

Publisher(s):Springer
Place of Publication:Berlin
Language:eng
Publication Date:©2011

Notes

New, completely revised, updated and enlarged edition of: Spin glasses : a challenge for mathematicians / Michel Talagrand. 2003.

The Physical Object

Description:1 online resource (xii, 629 pages)

Edition Identifiers

ISBN:9783642222535, 3642222536
DOI:10.1007/978-3-642-22253-5
oclc:ocn755538109
LC Classification:QC176.8.S68
Dewey Decimal:530.4/1

Part I. Advanced replica-symmetry. The Gardner formula for the sphere -- The Gardner formula for the discrete cube -- The Hopfield model -- The SK Model without external field -- Part II. Low temperature. The Ghirlanda-Guerra identities -- The high-temperature region of the SK model -- The Parisi formula -- The Parisi solution -- The p-spin interaction model -- Appendix: Elements of probability theory.