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Real-Space Renormalization

  • Theodore W. Burkhardt
  • J. M. J. van Leeuwen

Part of the Topics in Current Physics book series (TCPHY, volume 30)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. T. W. Burkhardt, J. M. J. van Leeuwen
    Pages 1-31
  3. R. H. Swendsen
    Pages 57-86
  4. G. F. Mazenko, O. T. Valls
    Pages 87-117
  5. P. Pfeuty, R. Jullien, K. A. Penson
    Pages 119-147
  6. H. E. Stanley, P. J. Reynolds, S. Redner, F. Family
    Pages 169-206
  7. Back Matter
    Pages 207-216

About this book

Introduction

The renormalization-group approach is largely responsible for the considerable success which has been achieved in the last ten years in developing a complete quantitative theory of phase transitions. Before, there was a useful physical picture of phase transitions, but a general method for making accurate quantitative predictions was lacking. Existent theories, such as the mean-field theory of Landau, sometimes reproduce phase diagrams reliably but were known to fail qualitatively near critical points, where the critical behavior is particularly interesting be­ cause of its universal character. In the mid 1960's Widom found that the singularities in thermodynamic quanti­ ties were well described by homogeneous functions. Kadanoff extended the homogeneity hypothesis to correlation functions and linked it to the idea of scale invariance. In the early 1970's Wilson showed how Kadanoff's rescaling could be explicitly carried out near the fixed point of a flow in Hamiltonian space. He made the first practical renormalization-group calculation of the flow induced by the elimination of short-wave-length Fourier components of the order-parameter field. The univer­ sality of the critical behavior emerges in a natural way in this approach, with a different fixed point for each universality class. The discovery by Wilson and Fisher of a systematic expansion procedure in E for a system in d = 4 - E dimen­ sions was followed by a cascade of calculations of critical quantities as a function of d and of the order-parameter dimensionality n.

Keywords

Renormalization group Renormierung Space behavior field theory phase phase diagram phase transition renormalization system

Editors and affiliations

  • Theodore W. Burkhardt
    • 1
    • 2
  • J. M. J. van Leeuwen
    • 3
  1. 1.Institut Laue-LangevinGrenoble CédexFrance
  2. 2.Department of PhysicsTemple UniversityPhiladelphiaUSA
  3. 3.Laboratorium voor Technische NatuurkundeTechnische Hogeschool DelftDelftThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-81825-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 1982
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-81827-1
  • Online ISBN 978-3-642-81825-7
  • Series Print ISSN 0342-6793
  • Buy this book on publisher's site