This volume is the first part of a treatise on Spin Glasses. The second part is Vol. 55 of the Ergebnisse series. The first edition was published as Vol. 46 of the same series ((978-3-540-00356-4).
2nd, rev. and enlarged ed. 2011, XVIII, 485 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 a 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
This first volume presents the basic results and methods
This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians". This new edition will appear in two volumes, the present first volume presents the basic results and methods, the second volume is expected to appear in 2011. 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 first volume of this new and completely rewritten edition presents six fundamental models and the basic techniques to study them.
Content Level »Research
Keywords »Disordered Systems - Hopfield Model - Mean Field Models - Random Structures - Sherrington Kirkpatrick Model