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Mathematics - Probability Theory and Stochastic Processes | Mean Field Models for Spin Glasses - Volume II: Advanced Replica-Symmetry and Low Temperature

Mean Field Models for Spin Glasses

Volume II: Advanced Replica-Symmetry and Low Temperature

Talagrand, Michel

Originally published as Volume 46 in series "Ergebnisse der Mathematik"

2nd ed. 2011, XII, 632 p.

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  • 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.

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.

Content Level » Research

Keywords » Disordered Systems - Hopfield Model - Mean Field Models - Random Structures - Sherrington Kirkpatrick Model

Related subjects » Materials - Probability Theory and Stochastic Processes - Theoretical, Mathematical & Computational Physics

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