Structural Elements in Particle Physics and Statistical Mechanics PDF
Preview 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 contem porary 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 ..r n 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 con junction with NATO Scientific Affairs Division A Life Sciences Plenum Publishing Corporation B Physics London and New York C Mathematical and D. Reidel Publishing Company Physical Sciences Dordrecht, The Netherlands and Hingham, Massachusetts, USA D Behavioral and Martinus Nijhoff Publishers Social Sciences The Hague, The Netherlands E Applied Sciences Structural Elements in Particle Physics and Statistical Mechanics Edited by J. Honerkamp K. Pohlmeyer H. Romer and 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 Breis gau, 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 Organiza tion. 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, name ly 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 - lectures and seminars - are contained in this volume. 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 The ories. 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-Wurttem berg. 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 Secre tary. 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 J. Honerkamp February 1982 K. Pohlmeyer H. Romer CONTENTS Connectivity: a primer in phase transitions and critical phenomena for students of particle physics 1 H. Eugene Stanley Algebraic aspects of exact models 43 M. Gaudin Elementary methods for statistical systems, mean field, large n, and duality 61 C. Itzykson Quantum scattering transformation 93 L. D. Faddeev Phases in gauge theories 115 S. Yankielowicz Unification of gauge and gravity interactions from compositeness 141 G. Veneziano Strong CP violation and axions 159 C. Jarlskog Non-linear mechanics of a string in a viscous noisy environment 171 w. G. Faris and G. Jona-Lasinio Some new integrable models in field theory and statistical mechanics 179 H. de Vega Calculating the large N phase transition in lattice gauge theories 191 S. Samuel vii viii CONTENTS Excitation spectrum of ferromagnetic xxz-chains 201 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 213 E. Stoll and T. Schneider Polyacetylene: a real material linking condensed matter and field theory 217 D. K. Campbell The hidden fermions in Z(2) theories 229 M. Srednicki Remarks on alternative lattice actions and phase structure of lattice models 241 H. Grosse Finite-size scaling theory 249 V. Ri ttenberg Anderson transition and nonlinear a-models 259 F. Wegner Functional integration for kinks and disord,er variables 261 B. Schroer Continuum (scaling) limits of lattice field theories (triviality of A~4 in d(~) 4 dimensions) 273 J. Frohlich Schrodinger representation in renormalizable quantum field theory 287 K. Symanzik 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 ix Radiative symmetry breaking in grand unified theories 327 N. Dragon, B. Stech Ground state metamorphosis for Yang-Mills fields on a finite periodic lattice 339 A. Gonzalez-Arroyo, J. Jurkiewicz, and C. P. Korthals-Altes Lattice Fermions and Monte Carlo Simulations 359 P. Hasenfratz Index 367 CONNECTIVITY: A PRIMER IN PHASE TRANSITIONS AND CRITICAL PHENOMENA FOR STUDENTS OF PARTICLE PHYSICS H. Eugene Stanley* Center for Polymer Studies** and Department of Physics Boston University, Boston, Massachusetts 02215 USA When the organizers of this Advanced Study Institute on "Structural Elements in Particle Physics and Statistical Mechanics" asked me to present 3 hours of introductory material on critical phenomena, I accepted happily because of the opportunity clearly afforded to broaden my understanding of the important cross-disciplinary overlaps between particle physics and critical phenomena. Now that I find myself standing in front of such an esteemed group of scholars, I am having misgivings. There is hardly anything that I can say here that some of you could not say betterl Moreover, the field of phase transitions and critical phenomena has become so vast that I truthfully do not know just where to begin. Therefore I shall begin at the beginning--I shall assume that some of you, at least, have no prior knowledge of my field and I shall attempt to describe some of the basic methods and results. My presentation shall focus on the overall theme of connectivity, since this is the topic of much of my own research and since most of the concepts of phase transitions can be easily illustrated with the paradigm of connectivity--the percolation problem. *John Simon Guggenheim Memorial Fellow, 1980-1981. **Supported in part by grants from ARO, ONR, and NSF.
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