Mean Field Models for Spin Glasses

This is a revised, updated and enlarged edition of Volume II of the author's book "Spin Glasses: A Challenge for Mathematicians" designed to introduce this exciting work to the math-minded reader, in a rigorous manner requiring no knowledge of any physics.

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.

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

Inhalt
Part I. Advanced Replica-Symmetry. - The Gardener Formula for the sphere. - The Gardener 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. - References. - Index.