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Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory

  • Roberto Fernández
  • Jürg Fröhlich
  • Alan D. Sokal

Part of the Texts and Monographs in Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Critical phenomena, quantum field theory, random walks and random surfaces: Some perspectives

    1. Front Matter
      Pages 1-1
    2. Roberto Fernández, Jürg Fröhlich, Alan D. Sokal
      Pages 3-36
    3. Roberto Fernández, Jürg Fröhlich, Alan D. Sokal
      Pages 37-52
    4. Roberto Fernández, Jürg Fröhlich, Alan D. Sokal
      Pages 53-57
    5. Roberto Fernández, Jürg Fröhlich, Alan D. Sokal
      Pages 59-77
    6. Roberto Fernández, Jürg Fröhlich, Alan D. Sokal
      Pages 79-99
    7. Roberto Fernández, Jürg Fröhlich, Alan D. Sokal
      Pages 101-115
    8. Roberto Fernández, Jürg Fröhlich, Alan D. Sokal
      Pages 117-178
  3. Random-walk models and random-walk representations of classical lattice spin systems

    1. Front Matter
      Pages 179-179
    2. Roberto Fernández, Jürg Fröhlich, Alan D. Sokal
      Pages 181-187
    3. Roberto Fernández, Jürg Fröhlich, Alan D. Sokal
      Pages 189-203
    4. Roberto Fernández, Jürg Fröhlich, Alan D. Sokal
      Pages 205-211
    5. Roberto Fernández, Jürg Fröhlich, Alan D. Sokal
      Pages 213-227
    6. Roberto Fernández, Jürg Fröhlich, Alan D. Sokal
      Pages 229-272
  4. Consequences for critical phenomena and quantum field theory

    1. Front Matter
      Pages 273-273
    2. Roberto Fernández, Jürg Fröhlich, Alan D. Sokal
      Pages 275-295
    3. Roberto Fernández, Jürg Fröhlich, Alan D. Sokal
      Pages 297-366
    4. Roberto Fernández, Jürg Fröhlich, Alan D. Sokal
      Pages 367-403
  5. Back Matter
    Pages 405-444

About this book

Introduction

Simple random walks - or equivalently, sums of independent random vari­ ables - have long been a standard topic of probability theory and mathemat­ ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk,were introduced into theoretical polymer physics, and gradu­ ally came to serve as a paradigm for the general theory of critical phenomena. In the past decade, random-walk expansions have evolved into an important tool for the rigorous analysis of critical phenomena in classical spin systems and of the continuum limit in quantum field theory. Among the results obtained by random-walk methods are the proof of triviality of the cp4 quantum field theo­ ryin space-time dimension d (::::) 4, and the proof of mean-field critical behavior for cp4 and Ising models in space dimension d (::::) 4. The principal goal of the present monograph is to present a detailed review of these developments. It is supplemented by a brief excursion to the theory of random surfaces and various applications thereof. This book has grown out of research carried out by the authors mainly from 1982 until the middle of 1985. Our original intention was to write a research paper. However, the writing of such a paper turned out to be a very slow process, partly because of our geographical separation, partly because each of us was involved in other projects that may have appeared more urgent.

Keywords

Gleichhewichtsstatistik Quantenfeldtheorie Wahrscheinlichkeitstheorie mathematical physics mathematische Physik quantum field theory statistical (equilibrium) dynamics

Authors and affiliations

  • Roberto Fernández
    • 1
  • Jürg Fröhlich
    • 1
  • Alan D. Sokal
    • 2
  1. 1.Institut für Theoretische PhysikETH HönggerbergZürichSwitzerland
  2. 2.Department of PhysicsNew York UniversityNew YorkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-02866-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-02868-1
  • Online ISBN 978-3-662-02866-7
  • Series Print ISSN 1864-5879
  • Series Online ISSN 1864-5887
  • Buy this book on publisher's site