Scale Invariance From Phase Transitions to Turbulence
During a century, from the Van der Waals mean field description (1874) of gases to the introduction of renormalization group (RG techniques 1970), thermodynamics and statistical physics were just unable to account for the incredible universality which was
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Annick Lesne
Michel Lagu¨es
Scale Invariance From Phase Transitions to Turbulence
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Dr. Annick Lesne Universit´e Paris VI Labo. Physique Th´eorique de la Mati`ere Condens´ee (LPTMC) place Jussieu 4 75252 Paris Cedex 05 France [email protected]
Michel Lagu¨es ESPCI rue Vauquelin 10 75231 Paris France [email protected]
Translated by Rhoda J. Hawkins, PhD. The original, French edition was published under the title ‘Invariances d’´echelle: Des changements d’´etats a` la turbulence’ c 2003, 2008 Editions Belin, France ISBN 978-3-642-15122-4 e-ISBN 978-3-642-15123-1 DOI 10.1007/978-3-642-15123-1 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011940326 c Springer-Verlag Berlin Heidelberg 2012 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Foreword
The opalescence of a fluid near its critical point has been a matter of curiosity for more than 100 years. However, the organisation of a fluid as it wavers between a liquid and a vapour was only understood 40 years ago – thanks to a profound insight by Leo Kadanoff in what was a major cultural achievement. We also know of other “self-similar” systems: fractals (structures resulting from quite simple geometrical constructions) and turbulent flows (which we still struggle to control). But the case of critical points has become the key example: difficult but accessible to reasoning and all embracing enough to manifest widely varying families of behaviours. The techniques of calculation (the “renormalisation group”) are given in many works and brought together in the fine book by Toulouse and Pfeuty. But a book giving the panorama was needed: this is it. It starts with liquids and gases but it also shows the multiple scales that we meet in Brownian motion, flexible polymers or percolation clusters. Furthermore, the book is bold enough to address questions that are still open: cuprate superconductors, turbulence, etc. The most controversial question, which appears in the final chapter, is that of “self-organised criticality”. For some this is a whole new world, and for others a world of mere words. But in any case, this book gi
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