Spin Glasses
Spin glass theory is going through a stunning period of progress while finding exciting new applications in areas beyond theoretical physics, in particular in combinatorics and computer science. This collection of state-of-the-art review papers written by
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Erwin Bolthausen Anton Bovier (Eds.)
Spin Glasses
1900
Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1900
Erwin Bolthausen, Anton Bovier (Eds.)
Spin Glasses
ABC
Editors Erwin Bolthausen Mathematics Institute University of Zürich Winterthurerstraße 190 8057 Zürich, Switzerland e-mail: [email protected] Anton Bovier Weierstraß Institute for Applied Analysis and Stochastics Mohrenstraße 39 10117 Berlin Germany and Institute for Mathematics Berlin University of Technology Straße des 17. Juni 136 10623 Berlin Germany e-mail: [email protected] Library of Congress Control Number: 2006932484 Mathematics Subject Classification (2000): 82B44, 82C44, 82B20, 60K35, 60K37 ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN-10 3-540-40902-5 Springer Berlin Heidelberg New York ISBN-13 978-3-540-40902-1 Springer Berlin Heidelberg New York DOI 10.1007/3-540-40902-5 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting by the editors and SPi using a Springer LATEX package Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper
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Preface
Spin glasses have become a paradigm for highly complex disordered systems. In the 1960’ies, certain magnetic alloys were found to have rather anomalous magnetic and thermal properties that seemed to indicate the existence of a new kind of phase transition, clearly distinct from conventional ferromagnetic materials. The origin of these anomalies was soon deemed to lie in two features: the presence of competing signs in the two-body interactions, and the disorder in the positions of the magnetic atoms in the alloy. This has led to the modelling of such materials in the form of spin-systems with random interactions. In the 1970ies, two principle models were proposed: the Edwards-Anderson model, which is a lattice spin system with random nearest neighbor interactions and as such is the randomized version of the classical Ising model; and the Sherrington-Kirkpatrick model, proposed as a mean field model, where all spins interact with each other on equal footing, whic
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