Mean Field Models for Spin Glasses
Volume I: Basic Examples
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Beschreibung
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.
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. Includes supplementary material: sn.pub/extras
Autor*in
Michel Talagrand
Themen in »Mean Field Models for Spin Glasses«
Disordered Systems Hopfield Model Mean Field Models Random Structures Sherrington Kirkpatrick Model
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From the reviews:
“It builds stone by stone a remarkable construction, revealing at each step a new piece of the fascinating picture of mean-field spin glass models. … Enlightening explanations, written with strong commitment, help the reader to grasp the general line of thought before entering into the computations … . With its depth and proficiency of important techniques, this book opens new perspectives on probability theory and the statistical mechanics of disordered systems. It will be a source of inspiration for generations of mathematicians.” (Francis Comets, Mathematical Reviews, Issue 2012 c)()