Spin Glasses: Statics and Dynamics Summer School, Paris 2007
Over the last decade, spin glass theory has turned from a fascinating part of t- oretical physics to a ?ourishing and rapidly growing subject of probability theory as well. These developments have been triggered to a large part by the mathem- ical underst
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Series Editors Charles Newman Sidney I. Resnick
Spin Glasses: Statics and Dynamics Summer School, Paris 2007
Anne Boutet de Monvel Anton Bovier Editors
Birkhäuser Basel · Boston · Berlin
Editors: Anne Boutet de Monvel Institut de Mathématique de Jussieu Université Paris Diderot Paris 7 175 rue du Chevaleret 75013 Paris France e-mail: [email protected]
Anton Bovier Institut für Angewandte Mathematik Rheinische Friedrich-WilhelmsUniversität Wegelerstrasse 6 53115 Bonn Germany e-mail: [email protected]
2000 Mathematics Subject Classification: 82-06, 82B44
Library of Congress Control Number: 2009933494 Bibliographic information published by Die Deutsche Bibliothek. Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de
ISBN 978-3-7643-8999-4 Birkhäuser Verlag AG, Basel · Boston · Berlin 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, re-use of illustrations, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use whatsoever, permission from the copyright owner must be obtained.
© 2009 Birkhäuser Verlag AG Basel · Boston · Berlin P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced from chlorine-free pulp. TCF ∞ Printed in Germany ISBN 978-3-7643-8999-4
e-ISBN 978-3-7643-9891-0
987654321
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Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii
Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
List of Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xi
Part I: Mean Field A. Bovier and I. Kurkova A Short Course on Mean Field Spin Glasses . . . . . . . . . . . . . . . . . . . . . . . . . G. Ben Arous and A. Kuptsov REM Universality for Random Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . ˇ y J. Cern´ Another View on Aging in the REM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 45 85
P. Contucci, C. Giardin` a and H. Nishimori Spin Glass Identities and the Nishimori Line . . . . . . . . . . . . . . . . . . . . . . . . . 103 L. De Sanctis and S. Franz Self-averaging Identities for Random Spin Systems . . . . . . . . . . . . . . . . . . . 123 T. Rizzo Chaos in Mean-field Spin-glass Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 A. Hanen A non Gaussian Limit Law for the Covariances of Spins in a SK Model with an External Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
159
A. Hanen A Limit Theorem for Mean Magnetisation in the Sherrington–Kirkpatrick Model with an External Field . . . . . . . . . . . . . . . 177
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