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Models in Statistical Physics and Quantum Field Theory

  • Harald Grosse

Part of the Trieste Notes in Physics book series (TRIESTE)

Table of contents

  1. Front Matter
    Pages I-X
  2. Harald Grosse
    Pages 1-12
  3. Harald Grosse
    Pages 13-44
  4. Harald Grosse
    Pages 45-68
  5. Harald Grosse
    Pages 69-100
  6. Harald Grosse
    Pages 101-113
  7. Harald Grosse
    Pages 114-148
  8. Back Matter
    Pages 149-151

About this book

Introduction

In these lectures we summarize certain results on models in statistical physics and quantum field theory and especially emphasize the deep relation­ ship between these subjects. From a physical point of view, we study phase transitions of realistic systems; from a more mathematical point of view, we describe field theoretical models defined on a euclidean space-time lattice, for which the lattice constant serves as a cutoff. The connection between these two approaches is obtained by identifying partition functions for spin models with discretized functional integrals. After an introduction to critical phenomena, we present methods which prove the existence or nonexistence of phase transitions for the Ising and Heisenberg models in various dimensions. As an example of a solvable system we discuss the two-dimensional Ising model. Topological excitations determine sectors of field theoretical models. In order to illustrate this, we first discuss soliton solutions of completely integrable classical models. Afterwards we dis­ cuss sectors for the external field problem and for the Schwinger model. Then we put gauge models on a lattice, give a survey of some rigorous results and discuss the phase structure of some lattice gauge models. Since great interest has recently been shown in string models, we give a short introduction to both the classical mechanics of strings and the bosonic and fermionic models. The formulation of the continuum limit for lattice systems leads to a discussion of the renormalization group, which we apply to various models.

Keywords

Renormalization group chaos magnetism phase transition polymer quantum field quantum field theory renormalization scattering soliton statistical physics

Authors and affiliations

  • Harald Grosse
    • 1
  1. 1.Institut für Theoretische PhysikUniversität WienWienAustria

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-83504-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-19383-8
  • Online ISBN 978-3-642-83504-9
  • Buy this book on publisher's site