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Real-Space Renormalization

  • Book
  • © 1982

Overview

Editors:
  1. Theodore W. Burkhardt

    1. Institut Laue-Langevin, Grenoble Cédex, France
      Department of Physics, Temple University, Philadelphia, USA

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  2. J. M. J. Leeuwen

    1. Laboratorium voor Technische Natuurkunde, Technische Hogeschool Delft, Delft, The Netherlands

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    You can also search for this editor in PubMed   Google Scholar

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XIII
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  2. Progress and Problems in Real-Space Renormalization

    • T. W. Burkhardt, J. M. J. van Leeuwen
    Pages 1-31

  3. Bond-Moving and Variational Methods in Real-Space Renormalization

    • T. W. Burkhardt
    Pages 33-56

  4. Monte Carlo Renormalization

    • R. H. Swendsen
    Pages 57-86

  5. The Real Space Dynamic Renormalization Group

    • G. F. Mazenko, O. T. Valls
    Pages 87-117

  6. Renormalization for Quantum Systems

    • P. Pfeuty, R. Jullien, K. A. Penson
    Pages 119-147

  7. Application of the Real-Space Renormalization to Adsorbed Systems

    • M. Schick
    Pages 149-168

  8. Position-Space Renormalization Group for Models of Linear Polymers, Branched Polymers, and Gels

    • H. E. Stanley, P. J. Reynolds, S. Redner, F. Family
    Pages 169-206

  9. Back Matter

    Pages 207-216
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Keywords

About this book

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.

Editors and Affiliations

  • Institut Laue-Langevin, Grenoble Cédex, France

    Theodore W. Burkhardt

  • Department of Physics, Temple University, Philadelphia, USA

    Theodore W. Burkhardt

  • Laboratorium voor Technische Natuurkunde, Technische Hogeschool Delft, Delft, The Netherlands

    J. M. J. Leeuwen

Bibliographic Information

  • Book Title: Real-Space Renormalization

  • Editors: Theodore W. Burkhardt, J. M. J. Leeuwen

  • Series Title: Topics in Current Physics

  • DOI: https://doi.org/10.1007/978-3-642-81825-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1982

  • Softcover ISBN: 978-3-642-81827-1Published: 08 December 2011

  • eBook ISBN: 978-3-642-81825-7Published: 06 December 2012

  • Series ISSN: 0342-6793

  • Edition Number: 1

  • Number of Pages: XIV, 216

  • Topics: Thermodynamics, Complex Systems, Statistical Physics and Dynamical Systems

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