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Introduction to a Renormalisation Group Method

  • Roland Bauerschmidt
  • David C. Brydges
  • Gordon Slade
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2242)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Spin Systems and Critical Phenomena

    1. Front Matter
      Pages 1-1
    2. Roland Bauerschmidt, David C. Brydges, Gordon Slade
      Pages 3-28
    3. Roland Bauerschmidt, David C. Brydges, Gordon Slade
      Pages 29-36
    4. Roland Bauerschmidt, David C. Brydges, Gordon Slade
      Pages 37-52
    5. Roland Bauerschmidt, David C. Brydges, Gordon Slade
      Pages 53-65
  3. The Renormalisation Group: Perturbative Analysis

    1. Front Matter
      Pages 67-67
    2. Roland Bauerschmidt, David C. Brydges, Gordon Slade
      Pages 69-88
    3. Roland Bauerschmidt, David C. Brydges, Gordon Slade
      Pages 89-104
  4. The Renormalisation Group: Nonperturbative Analysis

    1. Front Matter
      Pages 105-105
    2. Roland Bauerschmidt, David C. Brydges, Gordon Slade
      Pages 107-121
    3. Roland Bauerschmidt, David C. Brydges, Gordon Slade
      Pages 123-138
    4. Roland Bauerschmidt, David C. Brydges, Gordon Slade
      Pages 139-149
    5. Roland Bauerschmidt, David C. Brydges, Gordon Slade
      Pages 151-179
  5. Self-Avoiding Walk and Supersymmetry

    1. Front Matter
      Pages 181-181
    2. Roland Bauerschmidt, David C. Brydges, Gordon Slade
      Pages 183-210
  6. Appendices

    1. Front Matter
      Pages 211-211
    2. Roland Bauerschmidt, David C. Brydges, Gordon Slade
      Pages 213-233
    3. Roland Bauerschmidt, David C. Brydges, Gordon Slade
      Pages 235-269
  7. Back Matter
    Pages 271-283

About this book

Introduction

This is a primer on a mathematically rigorous renormalisation group theory, presenting mathematical techniques fundamental to renormalisation group analysis such as Gaussian integration, perturbative renormalisation and the stable manifold theorem. It also provides an overview of fundamental models in statistical mechanics with critical behaviour, including the Ising and φ4 models and the self-avoiding walk.

The book begins with critical behaviour and its basic discussion in statistical mechanics models, and subsequently explores perturbative and non-perturbative analysis in the renormalisation group. Lastly it discusses the relation of these topics to the self-avoiding walk and supersymmetry.

Including exercises in each chapter to help readers deepen their understanding, it is a valuable resource for mathematicians and mathematical physicists wanting to learn renormalisation group theory.

Keywords

Gaussian Integration Gaussian Measures Ising Model Perturbative Renormalisation Phi^4 Spin Model Renormalisation Group Method Scaling Limits Self-avoiding Walk Stable Manifold Theorem Theory of Critical Phenomena

Authors and affiliations

  • Roland Bauerschmidt
    • 1
  • David C. Brydges
    • 2
  • Gordon Slade
    • 3
  1. 1.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeCambridgeUK
  2. 2.Department of MathematicsThe University of British ColumbiaVancouverCanada
  3. 3.Department of MathematicsThe University of British ColumbiaVancouverCanada

Bibliographic information

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