Progress in Physics Vol.ll

Edited by A. Jaffe, G. Parisi, and D. Ruelle

Springer Science+Business Media, LLC

Critical Phenomena 1983 Bra~ov School Conference

Valentin Ceau~escu, Gabriel Costache, and Vladimir Georgescu, editors

Springer Science+Business Media, LLC 1985

Editors:

Valentin Ceau~escu Gabriel Costache Vladimir Georgescu Central Institute of Physics Bucharest, POB MG6 (Romania)

Library of Congress Cataloging in Publication Data

Bra~ov School Conference (1983 : Poiana Bra~ov, Romania) Critical phenomena.

(Progress in physics ; vol. 11) 1. Critical phenomena (Physics) -- Congresses.

2. Phase transformations (Statistical physics) --Congresses. I. Ceau~escu, V. II. Costache, Gabriel, 1942- III. Georgescu, V. (Vladimir), 1947-IV. Title. V. Series: Progress in physics (Boston, Mass.) : v. 11. QC173.4.C74B73 1983 530 85-3861 ISBN 978-1-4899-6652-0

CIP-Kurztitelaufnahme der Deutschen Bibliothek

Critical phenomena : 1983 Bra~ov School conference I Valentin Ceau~escu ... , ed.

(Progress in physics ; Vol. 11) ISBN 978-1-4899-6652-0 ISBN 978-1-4899-6650-6 (eBook) DOI 10.1007/978-1-4899-6650-6

NE: Ceau~escu, Valentin [Hrsg.]; GT

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner.

© 1985 Springer Science+ Business Media New York Originally published by Birkhauser Boston, Inc. in 1985 Softcover reprint of the hardcover 1st edition 1985

ISBN 978-1-4899-6652-0

5

TABLE OF CONTENTS

I. CRITICAL PHENOMENA IN STATISTICAL '1ECHANICS AND QUANTU'1 FIELD THEORY

K.R. Ito - Kosterlitz-Thouless Transition and Mayer Expansion

C.Itzykson an J.M. Luck- Zeroes of the Partition

Function for Statistical Models on Regular and Hierarchical Lattices

E.Seiler - Phase Structure of Finite Temperature Gauge Theories

R.Seneor - Critical Phenomena in Three Dimensions C.J. Thompson - Random Spin Systems

I NV !TED SH1I NARS

R.Gielerak -On the Scaling Limits and DLR Equations in the Euclidean Field Theory

H. Kerler - Critical Behavior and Renormalization

of Quantum Fields

II. CRITICAL PHENOMEtlA IN ~'UCLEAR AND PARTICLE PHYSICS

R.Gilmore - Classical Limits and Critical Properties

B.G.Giraud - A Few Methods for the Theory of

Collective Motions and Collisions

A.B.Midgal - Some Critical Phenomena in Vacuum

III. RELATED TOPICS

H.Araki - Dynamic and Ergodic Properties of the

XY-Model

17

45

83

110

136

189

198

213

245

283

287

6

D.Iagolnitzer - Unitarity of Asymptotic Completeness Equations and Analytic Structure of the S Matrix

and Green Functions A.Patrascioiu - Dynamical Systems and Statistical

r1echani cs

IV. EXACTLY SOLUBLE MODELS

P.P.Kulish- Quantum Spectral Transform J.M.r1aillard - Star-Triangle and Inversion Relations

in Statistical Mechanics

A.B.Zamolodchikov - Conformal Bootstrap in Two Dimensions

r1.Sato, Y.Sato - Universal Grassman Manifold and Integrable Systems

315

337

351

375

402

7

PREFACE

The courses of the 1983 Poiana Brasov Summer School were mainly devoted to the theory of phase transitions and critical phenomena. Our purpose was to evidentiate the mathematical structure of critical phe­nomena appearing in various areas of physics and the existence of some unifying structures behind them. This volume contains the lectures de­livered at the School arranged according to the following themes:

i) Phase transitions and critical phenomena in Statistical Mechanics (SM) and Quantum Field Theory (QFT).

ii) Collective motion and phase transitions in Nuclear and Par­ticle Physics.

iii) Exactly soluble models.

In spite of many efforts during the last 50 years we are still quite far from a general theory of phase transitions. Moreover the mathemati­cal understanding of critical phenomena in realistic models is still lacking. However there has been some progress in the description of these phenomena and this is certainly related to the transfer of methods from one branch of theoretical physics to another. This is particularly evident in St~ and QFT: the powerful Peierls argument developed origi­nally in SM allowed the description of the phase structure of some quan­tum field models; when combined with renormalization group ideas (origi­nating in QFT) it made possible the rigorous understanding of the Kosterlitz-Thouless transition. Also the spin wave concepts and the in­frared bounds have been used to analyze large classes of lattice models. It is thus difficult to separate nowadays papers dealing with critical phenomena in QFT from those in Sl·1 an:!a common mathematical structure is already emerging (e.g. see Seneors's lecture wnere the euclidean forma­lism of QFT provides the unifying frame).

Critical phenomena in Nuclear Physics appear mainly due to the com­

petition between single particle and collective properties of nuclear systems (i.e. sudden change in inertial parameters due to the transition from superfluid to normal phase, which occurs at high spins). Gilmore's

8

lecture emphasizes algebraic methods (groups of symmetry and coherent

states) while the lecture given by Giraud insists on a self-consistent treatment of the nucleus. Both of them rely on the role played by the mean field concept in the description of the nuclear ground states, which provides a natural foundation for exploration of dynamics. We re­

gret very much that a written version of Prof. Migdal's lecture in which the interplay of concepts from Particle, Nuclear and Statistical

Physics was used to describe critical phenomena in vacuum, has not been

submitted in due time for publication. The study of exactly soluble models has always been an important

source of insight in the understanding of phase transitions and criti­

cal phenomena. The recent developments in this area have been essential­

ly related to the appearance of new techniques of analysis of complete­

ly integrable systems, useful especially for low dimensional SM and

QFT models. The hope is that methods suitable to the study of higher di­mensional models will be found. Several lectures in this volume give

some perspective into this direction. The lecturershad typically three or four sessions to develop their

subject. The evident care which they brought to the preparation and

presentation of the lectures is gratefully acknowledged. Special thanks are due to Prof. Itzykson who, though unable to attend the conference, has been so kind to send us a written version of his lecture.

We wish to thank our colleagues from Central Institute of Physics -Bucharest who helped us in one way or another in the organization of the School. The enthusiasm with which Dr. N. Zamfir contributed effec­tively in the organizing process at Poiana Brasov is especially acknow­ledged. We are indebted to Prof. M. Ivascu, Director of the Central

Institute of Physics, for his permanent support of the School.

Last but not the least we are grateful to Mrs. Geta Uglai, the

technical secretary of the School, for the competence and efficiency of

her work during the organization of the School and the preparation

of this volume.

THE EDITORS

Bucharest, 1984

A..~GELESCU, N.

ANGHEL, A.T.

ANGHEL, V.

ARAKI, H.

ATANASIU, C.

BADEA, M.

BADKE, R.

BULGAC, A.

BUNDARU, M.

BUZULOIU, V.

CAPRINI-GOLOGAN,

CEAUSESCU, v. CIONGA, v.

Irinel

CIUBOTARU, Luminita

CORCIOVEI, A.

COSTACHE, G.

CZYZ, J.

DATCU, M.

DATOUSSAID, H.

DEM!ITH, t1.

DITA, P.

DOMITIAN, V.

DORLAS, T.C.

DUMITRESCU, B.O.

EFIMOV, G.

9

LIST OF PARTICIPANTS

Central Institute of Physics, Bucharest

ICPIAF, Cluj-Napoca

Institute for Nuclear Power Reactors,Pitesti

RIMS, Kyoto University

IPGG, Bucharest

Central Institute of Physics, Bucharest

University of Bonn

Central Institute of Physics, Bucharest

Central Institute of Physics, Bucharest

IPGG, Bucharest

Central Institute of Physics, Bucharest

Central Institute of Physics, Bucharest

Central Institute of Physics, Bucharest

Central Institute of Physics, Bucharest

Central Institute of Physics, Bucharest

Central Institute of Physics, Bucharest

Institute of Mathe~atics, 1-larsaw

Polytechnical Institute, Bucharest

University of Mons

Institute of Mathematics, Berlin

Central Institute of Physics, Bucharest

High School, Ploiesti

Inst.voor Theor.Natuurkunde, Groningen

Central Institute of Physics, Bucharest

Joint Institute for Nuclear Research, Dubna

FAZAKAS, A.

FAZIO, R.

FELDER, G.

GABITOV, I.

GALIN, Elena

GEORGESCU, V.

GIANNESSI, C.

GIELERAK, R.

GILMORE, R.

GIM.UD, B.

GRECU, D.

GRIGORE, R.D.

GROSU, Corina

GROSU, Marta

GRVNFELD, P .

GUSSI, G.

HATEGAN, C.

HRISTEA, M. R.

HOROI, M.

IACOBAS, A.

IAGOLNITZER, D.

IGLOI, F.

ION, B.D.

ISAR, A.

ITO, K.R.

IVANOV, M.

IXARU, L.

JIPA, A.

JURZAK, J ,p.

KERLER, W.

KISS-TOTH, T.

KULISH, p,p,

LUPU, D.

10

Central Institute of Physics, Bucharest

Institute of Physics, Catania

ETH, Zurich

Inst.of Phys. Acad.of Sci.of Kirgiz Republic

Central Institute of Physics, Bucharest

Central Institute of Physics, Bucharest

University of Pisa

University of Wroclaw

Drexel University , Philadelphia

CEN - Saclay

Central Institute of Physics, Bucharest

Central Institute of Physics, Bucharest

Computer Centre CIMIC, Bucharest

High School, Bucharest

Central Institute of Physics, Bucharest

Dept.of Math. - INCREST, Bucharest

Central Institute of Physics, Bucharest

Institute of Medicine, Bucharest

Central Institute of Physics, Bucharest

Institute of Medicine, Bucharest

CEN - Saclay

Central Res.Inst. for Physics, Budapest

Central Institute of Physics, Bucharest

Central Institute of Physics, Bucharest

Bedford College , London

Inst.for Nucl.Res.and Nucl.Energy, Sofia

Central Institute of Physics, Bucharest

Institute for Nuclear Power Reactors, Pitesti

University of Dijon

Philipps University, Marburg

Inst.for Theor.Phys., Budapest

Math.Inst."P.A.Steklov", Leningrad

ICPE, Bucharest

MAHM:>UD, H.

MAILLARD, J • M.

MANEA, Mihaela

MEk~IKOVA, Natasa

MIGDAL, A.B.

MIHALACHE, D.

MIHALACHE , G.

MIHUL, Eleonora

}10LA, I.

MOT, P.

NAIDIN, Andreea

NAPIORKOWSKI, M.

NENCIU, Alexandrina

NENCIU, G.

PARPALEA, M.

PAVEL, E.

PARLOG, M.

PATRASCIOIU, A.

PFITZNER, A.

PILLET, C.A.

PISO, M.

PLECHKO, V.

POPP, O.T.

PRIEZZHEV, V.

PURICE, R.

RADU, Doina

RAYCHEV, P.

ROSU, H.

SAKATA, F.

SARU, D.

SATO, M.

SATO, Yasuko

SEILER, E.

SENEOR, R.

SPINEANU, F.

11

Atomic Energy Establishment, Cairo

CEN - Saclay

High School, Brasov

Sci.Res.Inst. for Nucl.Physics, Moscow

"L.D.Landau" Institute, Moscow

Central Institute of Physics, Bucharest

University of Bucharest

Central Institute of Physics, Bucharest

Institute for Nuclear Power Reactors, Pitesti

Institute of Medicine, Bucharest

High School, Bucharest

University of Warsaw

Central Institute of Physics, Bucharest

Central Institute of Physics, Bucharest

High School, Brasov

CCSIT-MFS, Bucharest

Central Institute of Physics, Bucharest

University of Arizona, Tucson

Z.f.K., Rossendorf

ETH-Zurich

ICPE, Bucharest

Joint Institute for Nuclear Research, Dubna

Central Institute of Physics, Bucharest

Joint Institute for Nuclear Research, Dubna

Central Institute of Physics, Bucharest

Institute of Uedicine, Bucharest

Inst.for Nucl.Res. and Nucl.Energy, Sofia

Central Institute of Physics, Bucharest

University of Tokyo

ICPE, Bucharest

RIMS, Kyoto University

University of Ryukyus, Okinawa

Max-Planck Institute, Munchen

Ecole Politechnique, Palaiseau

Central Institute of Physics, Bucharest

STEINBRECHER, G.

STEUDEL, H.

STOENESCU, G.

STOICA, S.

STRATAN, G.

SUT5, A.

TATARU, L.O.

THOMPSON, C.J.

TOPOR, Nadia Marina

TRACHE, L.

TRACHE, Maria

URSU, I. I.

VINERSAN, J.

VISINESCU, Anca

VISINESCU, M.

VLAD, Madalina

WOLLENBERG, M.

WUNSCH, R.

YI-MIN, Jiang

ZAMFIR, N. V.

ZAMOLODCHIKOV, A.B.

ZIMMER, K.W.

12

University of Craiova

Zentr.Inst.f.Optik und Spektroskopie, Berlin

University of Craiova

Central Institute of Physics, Bucharest

Central Institute of Physics, Bucharest

Central Res.Inst.for Physics, Budapest

University of Craiova

University of Melbourne

High School, Bucharest

Central Institute of Physics, Bucharest

University of Bucharest

Central Institute of Physics, Bucharest

Institute of Medicine, Bucharest

Central Institute of Physics, Bucharest

Central Institute of Physics, Bucharest

Central Institute of Physics, Bucharest

Institute of Mathematics, Berlin

Z.f.K., Rossendorf

University of Bucharest

Central Institute of Physics, Bucharest

"L.D.Landau" Institute, Moscow

Central Institute of Physics, Bucharest

N. Angelescu

H. Datoussaid

G. Efimov

D. lagolnitzer

P.P. Kulish

A.B. Migdal

M. Napiorkowski

G. Nenciu

V.N. Plechko

V. Priezzhev

F. Sakata

13

SEMINARS

On the Critical Behavior of Semiinfinite Spherical Models

Critical Point Limit Law for Temperley's Continuous Model

Hadron Physics at Low Energies

Decay of Correlations and Limit Theorems

Graded Magnets

Problems of Nuclear Theory

Renormalization of Random Walks

Spontaneous Pair Creation in Strong External Fields

Scaling Relations for Critical Indices in the Case of Nonstandard Order Parameters

Phase Transitions in a Long Polymer Model

A New Type of "Phase Transition" Associated with Large Amplitude Nuclear Collective Motion