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Statistical Mechanics

An Introductory Graduate Course

  • A. J. Berlinsky
  • A. B. Harris

Part of the Graduate Texts in Physics book series (GTP)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. A. J. Berlinsky, A. B. Harris
      Pages 3-10
    3. A. J. Berlinsky, A. B. Harris
      Pages 11-25
    4. A. J. Berlinsky, A. B. Harris
      Pages 27-61
  3. Basic Formalism

    1. Front Matter
      Pages 63-63
    2. A. J. Berlinsky, A. B. Harris
      Pages 65-93
    3. A. J. Berlinsky, A. B. Harris
      Pages 95-118
    4. A. J. Berlinsky, A. B. Harris
      Pages 119-138
    5. A. J. Berlinsky, A. B. Harris
      Pages 139-175
  4. Mean Field Theory, Landau Theory

    1. Front Matter
      Pages 177-177
    2. A. J. Berlinsky, A. B. Harris
      Pages 179-200
    3. A. J. Berlinsky, A. B. Harris
      Pages 201-222
    4. A. J. Berlinsky, A. B. Harris
      Pages 223-261
    5. A. J. Berlinsky, A. B. Harris
      Pages 263-294
    6. A. J. Berlinsky, A. B. Harris
      Pages 319-344
    7. A. J. Berlinsky, A. B. Harris
      Pages 345-370
  5. Beyond Mean-Field Theory

    1. Front Matter
      Pages 371-371
    2. A. J. Berlinsky, A. B. Harris
      Pages 373-403
    3. A. J. Berlinsky, A. B. Harris
      Pages 405-440
    4. A. J. Berlinsky, A. B. Harris
      Pages 441-476
    5. A. J. Berlinsky, A. B. Harris
      Pages 477-493
    6. A. J. Berlinsky, A. B. Harris
      Pages 495-519
    7. A. J. Berlinsky, A. B. Harris
      Pages 521-556
    8. A. J. Berlinsky, A. B. Harris
      Pages 557-595
  6. Back Matter
    Pages 597-602

About this book

Introduction

In a comprehensive treatment of Statistical Mechanics from thermodynamics through the renormalization group, this book serves as the core text for a full-year graduate course in statistical mechanics at either the Masters or Ph.D. level. Each chapter contains numerous exercises, and several chapters treat special topics which can be used as the basis for student projects. 

The concept of scaling is introduced early and used extensively throughout the text. At the heart of the book is an extensive treatment of mean field theory, from the simplest decoupling approach, through the density matrix formalism, to self-consistent classical and quantum field theory as well as exact solutions on the Cayley tree. Proceeding beyond mean field theory, the book discusses exact mappings involving Potts models, percolation, self-avoiding walks and quenched randomness, connecting various athermal and thermal models. Computational methods such as series expansions and Monte Carlo simulations are discussed, along with exact solutions to the 1D quantum and 2D classical Ising models. The renormalization group formalism is developed, starting from real-space RG and proceeding through a detailed treatment of Wilson’s epsilon expansion. Finally the subject of Kosterlitz-Thouless systems is introduced from a historical perspective and then treated by methods  due to Anderson, Kosterlitz, Thouless and Young.

Altogether, this comprehensive, up-to-date, and engaging text offers an ideal package for advanced undergraduate or graduate courses or for use in self study.


Keywords

Wilson’s epsilon expansion renormalization group formalism Monte Carlo methods density matrix formalism quenched randomness mean field theory order parameters Landau Expansion Bose and Fermi Gases

Authors and affiliations

  • A. J. Berlinsky
    • 1
  • A. B. Harris
    • 2
  1. 1.Brockhouse Institute for Materials Research, Department of Physics and AstronomyMcMaster UniversityHamiltonCanada
  2. 2.Department of Physics and AstronomyUniversity of PennsylvaniaPhiladelphiaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-28187-8
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-030-28186-1
  • Online ISBN 978-3-030-28187-8
  • Series Print ISSN 1868-4513
  • Series Online ISSN 1868-4521
  • Buy this book on publisher's site