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This book contains a detailed and self-contained presentation of the replica theory of infinite range spin glasses. The authors also explain recent theoretical developments, paying particular attention to new applications in the study of optimization theory and neural networks. About two-thirds of the book are a collection of the most interesting and pedagogical articles on the subject.

"The authors give a masterly account of the work on the Sherrington-Kirkpatrick model in the first 85 pages. Such a summary cannot be found elsewhere, and much of our current understanding of the problem is due to the authors of this book and their collaborators".This is an important book, which every physics library should have. It is also good reading for anyone who wants to know about these aspects of the spin glass problem, and why "replica symmetry breaking'' and "ultrametricity'' may be important".Physics Today, 1988" a very useful source of relevant information on the progress achieved...

This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. It is accessible to graduate students and researchers without a specific training in any of these fields. The selected topics include spin glasses, error correcting codes, satisfiability, and are central to each field. The approach focuses on large random instances, adopting a common probabilistic formulation in terms of graphical models. It presents message passing algorithms like...