文档介绍：De Gruyter Studies in Mathematics 9
Editors
Carsten Carstensen, Berlin, Germany
Nicola Fusco, Napoli, Italy
Fritz Gesztesy, Columbia, USA
Niels Jacob, Swansea, United Kingdom
Karl-Hermann Neeb, Erlangen, Germany
Hans-Otto ii
Gibbs Measures and
Phase Transitions
Second Edition
De Gruyter
Mathematics Subject Classification 2010: Primary: 60-02, 82-02; Secondary: 82B05, 60K35,
82B20, 82B26.
ISBN 978-3-11-025029-9
e-ISBN 978-3-11-025032-9
ISSN 0179-0986
Library of Congress Cataloging-in-Publication Data
ii, Hans-Otto.
Gibbs measures and phase transitions / by Hans-Otto ii. —
[2nd ed.].
p. cm. —(De Gruyter studies in mathematics ; 9)
Includes bibliographical references and index.
ISBN 978-3-11-025029-9
1. Probabilities. 2. Phase transformations (Statistical physics)
3. Measure theory. I. Title.
2011
515'.42—dc22
2011006346
Bibliographic information published by the Deutsche Nationalbibliothek
The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie;
detailed bibliographic data are available in the at -.
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/New York
Printing and binding: Hubert & Co. GmbH & Co. KG, Göttingen
® Printed on acid-free paper
Printed in Germany
To my family
Preface
This book deals with systems of infinitely many random variables attached
to the vertices of a multi-dimensional lattice and depending on each other
according to their positions. The theory of such "spatial random systems with
interaction" is a rapidly growing branch of probability theory developed with
the goal of understanding the cooperative effects in large random systems.
The primary es from statistical physics. The range of applications
also includes various other fields such as biology, medicine, chemistry, and
economics, but this volume is only devoted to those concepts and results
which are significant for physics. In