Authors:
- Completely rewritten, updated and enlarged edition of Talagrand's Ergebnisse Vol. 46: "Spin Glasses: A Challenge for Mathematicians" (2003) in two volumes
- Will bring the reader with no previous knowledge of Spin Glasses to the frontier of current research
- The only fully rigorous treatise of this scale on the subject
- The present second volume contains a large amount of new results obtained after the publication of the first edition.
- Includes supplementary material: sn.pub/extras
Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (MATHE3, volume 55)
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Table of contents (9 chapters)
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Front Matter
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Advanced Replica-Symmetry
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Front Matter
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Back Matter
About this book
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.
Reviews
From the reviews of the second edition:
“This is the second volume of the author’s treatise Mean field models for spin glasses … . With its depth and profusion of important techniques, this book … opens new perspectives in probability theory and statistical mechanics of disordered systems. It will be a source of inspiration for generations of mathematicians.” (Francis Comets, Mathematical Reviews, November, 2013)
“This is the second volume of the treatise ‘Mean fields models for spin glasses’ and it is truly the continuation of the preceding one. … the book is a book of mathematics expanded around Hamiltonian. The main considered topics are the Gardner formula, the Hopfield model, the SK model, the Parisi formula and the p-spin interaction model. … This is truly a nice book of condensed mathematics.” (Guy Jumarie, Zentralblatt MATH, Vol. 1232, 2012)Authors and Affiliations
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Institut de mathématiques, UMR 7586 CNRS, Université Paris 6, Paris Cedex 05, France
Michel Talagrand
Bibliographic Information
Book Title: Mean Field Models for Spin Glasses
Book Subtitle: Volume II: Advanced Replica-Symmetry and Low Temperature
Authors: Michel Talagrand
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
DOI: https://doi.org/10.1007/978-3-642-22253-5
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag GmbH Berlin Heidelberg 2011
Hardcover ISBN: 978-3-642-22252-8Published: 14 August 2011
Softcover ISBN: 978-3-642-27094-9Published: 21 November 2013
eBook ISBN: 978-3-642-22253-5Published: 14 August 2011
Series ISSN: 0071-1136
Series E-ISSN: 2197-5655
Edition Number: 2
Number of Pages: XII, 632
Additional Information: Originally published as Volume 46 in series "Ergebnisse der Mathematik"
Topics: Probability Theory and Stochastic Processes, Mathematical Methods in Physics, Condensed Matter Physics