Structural Elements in Particle Physics and Statistical Mechanics

Structural Elements in Particle Physics and Statistical Mechanics

NATO ADVANCED STUDY INSTITUTES SERIES A series of edited volumes comprising multifaceted studies of contemporary scientific issues by some of the best scientific minds in the world, assembled in cooperation with NATO Scientific Affairs Division. Series 8: Physics Recent Volumes in this Series Volume 76-Metal Hydrides edited by Gust Bambakidis Volume 77-Nonlinear Phenomena at Phase Transitions and Instabilities edited by T. Riste Volume 78 - Excitations in Disordered Systems edited by M. F. Thorpe Volume 79-Artificial Particle Beams in Space Plasma Studies edited by Bj.. rn Grandal Volume 80-Quantum Electrodynamics of Strong Fields edited by W. Greiner Volume 81-Electron Correlations in Solids, Molecules, and Atoms edited by Jozef T. Devreese and Fons Brosens Volume 82-Structural Elements in Particle Physics and Statistical Mechanics edited by J. Honerkamp, K. Pohlmeyer, and H. Romer Volume 83 - Physics of Ion-Ion and Electron-Ion Collisions edited by F. Brouillard and J. W. McGowan Volume 84-Physical Processes in Laser-Materials Interactions edited by M. Bertolotti Volume 85 - Fundamental Interactions: Cargese 1981 edited by Maurice Levy, Jean-Louis Basdevant, David Speiser, Jacques Weyers, Maurice Jacob, and Raymond Gastmans This series is published by an international board of publishers in conjunction with NATO Scientific Affairs Division A Life Sciences B Physics C Mathematical and Physical Sciences D Behavioral and Social Sciences E Applied Sciences Plenum Publishing Corporation London and New York D. Reidel Publishing Company Dordrecht, The Netherlands and Hingham, Massachusetts, USA Martinus Nijhoff Publishers The Hague, The Netherlands

Structural Elements in Particle Physics and Statistical Mechanics Edited by J. Honerkamp K. Pohlmeyer and H. Romer Albert Ludwigs University Freiburg, Federal Republic of Germany PLENUM PRESS NEW YORK AND LONDON Published in cooperation with NATO Scientific Affairs Division

Library of Congress Cataloging in Publication Data NATO Advanced Summer Institute on Theoretical Physics (1981: Freiburg im Breisgau, Germany) Structural elements in particle physics and statistical mechanics. (NATO advanced study institutes series. Series B, Physics; v. 82) "Published in cooperation with NATO Scientific Affairs Division." "Proceedings of the NATO Advanced Summer Institute on Theoretical Physics... held August 31-September 11, 1981, in Freiburg"-Verso t.p. Includes bibliographical references and index. I. Particles (Nuclear physics)-congresses. 2. Statistical mechanics-congresses. I. Honerkamp, J. II. Pohlmeyer, K. III. Romer, H. IV. North Atlantic Treaty Organization. Division of Scientific Affairs. V. Title. VI. Series. QC793.N39 1981 539.7 82-10181 ISBN-13: 978-1-4613-3511-5 e-isbn-13: 978-1-4613-3509-2 DOl: 10.1007/978-1-4613-3509-2 Proceedings of the NATO Advanced Summer Institute on Theoretical Physics 1981, held August 31-September 11, 1981, in Freiburg, Federal Republic of Germany 1983 Plenum Press, New York Softcover reprint of the hardcover 1st edition 1983 A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. 10013 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher

PREFACE The NATO ADVANCED SUMMER INSTITUTE ON THEORETICAL PHYSICS 1981 was held in Freiburg, Germany from August 31st until September 11th 1981. It was the twelfth in a series of Summer Institutes organized by German Universities. Its main objective was a thorough comparison of structures and methods of two different branches of Theoretical Physics, namely Elementary Particle Physics and Statistical Mechanics, and the idea was to exhibit the structural similarities, to trace them until their origins, to compare solution and approximation schemes and to report on those new results and methods in either of the two branches which are indicative of an intimate connection between them. Thus stimulation of a deeper understanding and development of new Methods could be hoped for in both fields. The contributions to the Summer Institute - seminars - are contained in this volume. lectures and One group of them gives concise up-to-date information on basic topics in Statistical Mechanics and Phase Transitions, Dynamical Systems, Solvable Lattice Models and Lattice Gauge Theories. A second group is devoted to special topics which illustrate the interrelationship between Statistical Mechanics and Elementary Particle Physics, like topological quantum numbers on a lattice, model studies on the confinement problem, etc. Supplementary information on experimental implications and on neighbouring fields is provided in a third group. We are grateful that the Institute was sponsored by the NATO Advanced Study Institute program and that additional support was given by the Bundesministerium flir Wissenschaft und Technologie and the Ministerium flir Wissenschaft und Kunst in Baden-Wurttemberg. v

PREFACE It is a pleasure to thank the lecturers and seminar speakers for their carefully preparej contributions. Special thanks are due to Dr. M. Forger. the Scientific Secretary. to Dr. K. Fredenhagen. who did much redactionary work for these proceedings. Mrs. E. Rupp. our Conference Secretary and to Miss H. Kranz for typing large parts of the manuscripts. and all the others of the Physics Faculty of the University of Freiburg who were involved in the organization of this meeting. Freiburg February 1982 J. Honerkamp K. Pohlmeyer H. Romer

CONTENTS Connectivity: a primer in phase transitions and critical phenomena for students of particle physics H. Eugene Stanley Algebraic aspects of exact models M. Gaudin Elementary methods for statistical systems, mean field, large n, and duality C. Itzykson Quantum scattering transformation L. D. Faddeev Phases in gauge theories S. Yankielowicz Unification of gauge and gravity interactions from compositeness G. Veneziano Strong CP violation and axions C. Jarlskog 1 43 61 93 115 141 159 Non-linear mechanics of a string in a viscous environment w. G. Faris and G. Jona-Lasinio Some new integrable models in field theory and statistical mechanics H. de Vega noisy 171 179 Calculating the large N phase transition in lattice gauge theories S. Samuel 191 vii

viii Excitation spectrum of ferromagnetic xxz-chains T. Schneider and E. Stoll Computer simulations of a discontinuous phase transition and percolation clusters in the two- dimension~l one-spin-flip Ising model E. Stoll and T. Schneider Polyacetylene: a real material linking condensed matter and field theory D. K. Campbell The hidden fermions in Z(2) theories M. Srednicki Remarks on alternative lattice actions and phase structure of lattice models H. Grosse Finite-size scaling theory V. Ri ttenberg Anderson transition and nonlinear a-models F. Wegner Functional integration for kinks and disord,er variables B. Schroer Continuum (scaling) limits of lattice field theories (triviality of A~4 in d(~) 4 dimensions) J. Frohlich Schrodinger representation in renormalizable quantum field theory K. Symanzik CONTENTS 201 213 217 229 241 249 259 261 273 287 All self-dual multimonopoles for arbitrary gauge groups 301 W. Nahm Renormalization group aspects of 3-dimensional pure U(1) lattice gauge theory 311 M. Gopfert and G. Mack Mass splitting of the pseudo scalar mesons by Monte Carlo technique 317 P. di Vecchia

CONTENTS Radiative symmetry breaking in grand unified theories N. Dragon, B. Stech Ground state metamorphosis for Yang-Mills fields on a finite periodic lattice A. Gonzalez-Arroyo, J. Jurkiewicz, and C. P. Korthals-Altes Lattice Fermions and Monte Carlo Simulations P. Hasenfratz Index ix 327 339 359 367