In the 1980s, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". This rigorous book introduces this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics, and contains proofs in complete detail of much of what is rigorously known on spin glasses at the time of writing.
Disordered magnetic systems enjoy non-trivial properties which are different and richer than those observed in their pure, non-disordered counterparts. These properties dramatically affect the thermodynamic behaviour and require specific theoretical treatment. This book deals with the theory of magnetic systems in the presence of frozen disorder, in particular paradigmatic and well-known spin models such as the Random Field Ising Model and the Ising Spin Glass. This is a unified presentation using a field theory language which covers mean field theory, dynamics and perturbation expansion within the same theoretical framework. Particular emphasis is given to the connections between different approaches such as statics vs. dynamics, microscopic vs. phenomenological models. The book introduces some useful and little-known techniques in statistical mechanics and field theory. This book will be of great interest to graduate students and researchers in statistical physics and basic field theory.
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.
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