FereydoWlt Fami Mohamed Daoui - Han SCALING AND DISORDERED SYSTEMS This page is intentionally left blank International workshop and collection of articles honoring Professor Antonio Coniglio on the occasion of his 6othB irthday SCALING AND DISORDERED SYSTEMS Editors Fereydoon Family Emory University, USA Mohamed Daoud Centre &Etude Nucleaire, France Hans J. Herrmann ESPCI, France & IGll, Germany H. Eugene Stanley Boston University, USA world Scientific b New Jersey. London. Singapore. Hong Kong Published by World Scientific Publishing Co. Pte. Ltd. P 0 Box 128, Farrer Road, Singapore 912805 USA office: Suite lB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-PublicationD ata A catalogue record for this book is available from the British Library. SCALING AND DISORDERED SYSTEMS Copyright O 2002 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereoJ may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 981-02-4838-5 Printed in Singapore by Uto-Print It is a geat pleasure to dedicate this book of articles 61 honor of Professor Antonio Coniglio can the occasion of 60th Birthday, hAany of the articles me baed 011 research inspired by his ideas. Antonio 4s a great scientist in the tradition of the truly great; scientrs-ts, His ability to select just the right questions to pose has led to the remarkably blgh impact sf his work on many diverse branches of statistical physics. His creative approaches to solving complex problems cornbines deep physical intuition with matheaatical prowess of the first rank. Ant0;aio began his scientific co1zj;ributions in the field of many-body theory, concentrating on lm temperature properties of superBuid helium. In the early seventies, he began his studies of critical phenomena and the renormdization group, and de-veloped a generalized form of scaling1l9" that anticip2Lted muttifractality and multiscding - co~ceptsw liich played a significant role in a wide variety of fields rnmy years EatersT5 Ris coxlCributfons to scaling in phase transitions and critical phenomena naturally led to his classic papers on correlated percolation. He was among the first 60 introduce the concept of correlated percolation,'"which he later used to develop models for the sol-gel transition,""tG,39i176 Antonio "sn played a central role in the development of the theories of random and correlated percolation by formulating a general approach for the study of continuum and correlated percolation based on Meyer cluster exp=sican, enabling the extension of m8ny results from theory of fluids to perc~p1atlon.l~In~ ~re' laked works, he h a p roven rigorous fn- equa,lities between thermodynamic quantities and percolation quantities i~ the Ising model. Pa-hil is has led to the proof that lsing clusters percolate at the Ising critical poi~tin dimension but not necessa~iyi n higher dirnensi~ns.'~*~'~~' One sf Ar~to~iom'so st signilicant contributions which has led to important adl~a~eiens she theory sf percolation is the proof sf il relation betweea pair cc4nneetedness and singly connected bonds (also called red bofids), In psrticnlzr, he has prolied that one of the consequences of this relatior: is that the fractal dimension of she si~lglyc onnected boxids In. the incipiel~ti nfinite clusxer in random percolation is given by the 'thermal sealing exponellt- Based on these exact results he has made z. major contartbutiont o the characteriza"cion of the fractal structure of the percolation cluszer by putting or; a firm foundation the "nodes links and blobs model" for the incipiel~ti nfinite cluster, which is now accepted as "vhe standii,rd model for percolati~n,"*~"~ As a corollary to the above results, Antonio was able Po prove that the cromover critic4 exponents of the diit~te lsing model and Beisemberg mcidel are related: respectk;.eiy$ to the fractal dimension ajf the singly connected bonds and the resistnviBy ewpcnem7;.,, This ~roria.c larified and explained the experimental results in diluee ferromagnets and gave a geometricd b~terpretationo f W+ the esm crossot-er exponents were diEerera"t.33.3"50 In a seminal paper,25 Antonio and Bill Klein proposed a geometrical characterization of the Ising critical point in terms of new clusters (now known as the CK droplets) which have the properties of percolating at the Ising critical point with the Ising exponents.25~26~34~3g~104 This classic work is the foundation of the widely used Swendsen-Wang cluster dynamics algorithm. More recently, this cluster definition has received attention in QCD and also in explaining cluster fragmentation in nuclear matter. Another important work of Antonio was the analysis of the fractal structure of the CK droplets in the q-state Potts model. In this context, he provided exact values in two dimen- sions for the fractal dimension of the red bonds for any q. In particular for q = 0 he obtained the fractal dimension of the red bonds in the spanning tree.95 He also related the hyper- scaling breakdown, with the presence of infinitely many clusters above the uppercritical dimensi~nality.~~~~~~ Antonio has also made significant contributions to many aspects of the theory of diffusion- limited aggregation and the theory of multifractality research areas which have been - of central importance in understanding aggregation phenomena, disordered systems and fractals. For example, in collaboration with his colleagues, he was among the first to have contributed to the development and application of the concepts of multifractality and multiscaling in diffusion limited aggregation73~79~10a6n~d2 3in Percolation.74~83 Antonio has also made important contributions to the theory of phase separation. With Zannetti, he provided for the first time an analytical solution for the time-dependent Ginzburg Landau model, in the limit in which the number of components of the order parameter goes to infinity.lo3 Antonio and collaborators developed a microscopic "spin-glass" type of model that elucidates the phase diagram of a class of materials displaying high-temperature super- cond~ctivity.'T~ his contribution has received great attention in the field of high-temperature superconductivity and has been widely cited in the literature. More recently, Antonio has made important contributions to a number of topics re- lated to glasses and spin glasses.162~163~1H7e5 has also applied these models to granular material^,^^^^'^^^^^^ by developing with collaborators the frustrated percolation model which maps exactly the spin glass model into a geometrical model.'14 These models are playing an important role in describing granular materials and glasses, which are systems of con- siderable complexity and great current interest. Antonio is the voice of insight, reason, humor and honesty. Even as impressive as his contributions to physics are, what usually springs to one's mind is Antonio's great personal- ity and friendship. The joy of a meeting is always enhanced by his presence and thoughtful discussions and comments. The fact that all of scientists who came to his Paris meeting, came from the far corners of the globe without any financial support from the organizers attests to the honor in which Antonio is held by his colleagues. He is one of the truly highly respected figures in statistical physics. Fereydoon Family Department of Physics, Emory University, Atlanta Mohamed Daoud Centre d 'Etude Nucleaire, Saclay, France Hans J. Herrmann ESPCI, Paris and ICA I, Stuttgart, Germany H. Eugene Stanley Center for Polymer Physics, Boston University, Boston This page is intentionally left blank Professor Antonio Coniglio ANTONIO CONIGLIO: Curriculum Vitae Name: Antonio Coniglio Born: 5 April 1940 Education: - Laurea in Physics, cum laude (110/110) Naples University, November 1962 - Diploma Scuola di Perfesionamento, Naples University, November 1965 Employment: (1) Chaired Professorship in Statistical Mechanics, 1980 - Present - Research Professor of Physics, Center for Polymer Studies, Boston University, 1981 - Present - [Visiting Professor, Ecole Superieure de Physique et Chimie Industrielles, Paris, September-October 1992, September 1996, October 1997, January 19981 - [Visiting Professor, Service de Physique Theorique, C.E.N. Saclay, September 19891 - [Visiting Professor, Laboratoire Leon Brillouin C.E.N. Saclay, May 1980, April-July 19881 - [Visiting Professor, Centro Brasilero de Pesquisas Fisicas, January-February 1985, January 19871 - [Visiting Professor, St. Francis Xavier University, Antigonish, Nova Scotia, Canada, March 1985, James Chair Professor, March-April 19871 - Professore Incaricato Stabilizzato, 1974-1980, Naples University - [Visiting Assistant Professor of Physics, Center for Polymer Studies, Boston Univer- sity, sabbatical leave, 1977-19791 - Professore Incaricato, 1971-1974, Naples University - [Visiting Research Professor, King's College, London, November 1973-January 19741 - [Awarded the title LLLiberDa ocenza," 19721 (2) Researcher at King's College, London, 1970-1971 (3) Professore Incaricato, 1966-1968, 1969-1970 (4) Research Assistant, 1965-1966 Publicati ons 1. A. Coniglio, M. Marinaro and M. Maturi, "Stability Conditions for a Boson System Interacting with a Partly Repulsive and Partly Attractive Potential," Nuovo Cimento 40, 184 (1965). 2. A. Coniglio and M. Marinaro, "On Condensation for an Interacting Boson System," Nuovo Cimento 48, 249 (1967). 3. A. Coniglio and M. Marinaro, "Breakdown of Symmetry and Gapless Spectrum in Many-Boson Systems," Nuovo Cimento 48, 262 (1967). 4. A. Coniglio, Marinaro and B. Preziosi, "Phase Transition Between Partially Condensed Homogeneous and Periodic Systems," Nuovo Cimento 61, 25 (1969). 5. A. Coniglio, M. Marinaro and B. Preziosi, "On the Coexistence of Single and Two Particle Condensation in an Interacting Boson Gas," NUOVOC imento 63, 227 (1969). 6. A. Coniglio and R. Vasudevan, "Generalized Condensation of an Interacting Bose Gas with Pair Hamiltonian," Nuovo Cimento 70B,3 9 (1970).