The Sherrington-Kirkpatrick Model
The celebrated Parisi solution of the Sherrington-Kirkpatrick model for spin glasses is one of the most important achievements in the field of disordered systems. Over the last three decades, through the efforts of theoretical physicists and mathematician
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Dmitry Panchenko
The Sherrington-Kirkpatrick Model
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Dmitry Panchenko Department of Mathematics Texas A&M University College Station, TX, USA
ISSN 1439-7382 ISBN 978-1-4614-6288-0 ISBN 978-1-4614-6289-7 (eBook) DOI 10.1007/978-1-4614-6289-7 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2013931655 Mathematics Subject Classification: 60K35, 82B44, 60G15, 60G55, 60G57, 60G09, 82D30 © Springer Science+Business Media New York 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
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Preface
This book is an attempt to give, as much as possible, a self-contained presentation of some of the main ideas involved in the mathematical analysis of the Sherrington– Kirkpatrick model and closely related mixed p-spin models of spin glasses. Certain topics, such as the high-temperature region and phase transition, are not covered and can be found in the comprehensive manuscript of Michel Talagrand [66]. In 1975 David Sherrington and Scott Kirkpatrick introduced in [58] a model of a spin glass—a disordered magnetic alloy that exhibits unusual magnetic behavior. This model is also often interpreted as a question about a typical behavior of the optimization problem maxσ ∈ΣN HN (σ
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