Mean Field Models for Spin Glasses: Volume II: Advanced Replica-Symmetry and Low Temperature

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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.