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© 2011

Mean Field Models for Spin Glasses

Volume I: Basic Examples

Book

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Michel Talagrand
    Pages 1-149
  3. Michel Talagrand
    Pages 151-190
  4. Michel Talagrand
    Pages 191-236
  5. Michel Talagrand
    Pages 237-296
  6. Michel Talagrand
    Pages 297-323
  7. Michel Talagrand
    Pages 325-395
  8. Michel Talagrand
    Pages 397-433
  9. Back Matter
    Pages 435-485

About this book

Introduction

This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians". This new edition will appear in two volumes, the present first volume presents the basic results and methods, the second volume is expected to appear in 2011. 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 first volume of this new and completely rewritten edition presents six fundamental models and the basic techniques to study them.

Keywords

Disordered Systems Hopfield Model Mean Field Models Random Structures Sherrington Kirkpatrick Model

Authors and affiliations

  1. 1.Institut de mathématiquesUniversité Paris 6Paris Cedex 05France

About the authors

M. Talagrand is Research Director in CNRS, and Member of the French Academy of Sciences since 2004.

Bibliographic information

  • Book Title Mean Field Models for Spin Glasses
  • Book Subtitle Volume I: Basic Examples
  • Authors Michel Talagrand
  • Series Title Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
  • DOI https://doi.org/10.1007/978-3-642-15202-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-642-15201-6
  • Softcover ISBN 978-3-642-26598-3
  • eBook ISBN 978-3-642-15202-3
  • Edition Number 1
  • Number of Pages XVIII, 485
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information This volume is the first part of a treatise on Spin Glasses. The second part is Vol. 55 of the Ergebnisse series. The first edition was published as Vol. 46 of the same series ((978-3-540-00356-4).
  • Topics Probability Theory and Stochastic Processes
    Mathematical Methods in Physics
    Condensed Matter Physics
  • Buy this book on publisher's site
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Reviews

From the reviews:

“It builds stone by stone a remarkable construction, revealing at each step a new piece of the fascinating picture of mean-field spin glass models. … Enlightening explanations, written with strong commitment, help the reader to grasp the general line of thought before entering into the computations … . With its depth and proficiency of important techniques, this book opens new perspectives on probability theory and the statistical mechanics of disordered systems. It will be a source of inspiration for generations of mathematicians.” (Francis Comets, Mathematical Reviews, Issue 2012 c)