The Two-Dimensional Ising Model Second Edition

by McCoy, Barry M.; Wu, Tai Tsun

• ISBN13: 9780486493350
• ISBN10: 0486493350
• Format: Paperback
• Copyright: 2014-04-16
• Publisher: Dover Publications

Summary

"Of all the systems in statistical mechanics on which exact calculations have been performed," declare the authors of this text, "the two-dimensional Ising model is not only the most thoroughly investigated; it is also the richest and most profound." Originally published in 1973, this is the definitive survey of the Ising model, a mathematical model of ferromagnetism in statistical mechanics. This updated edition of the classic text features an extensive section on new developments. Geared toward advanced undergraduates and graduate students of physics, it is also suitable for physicists working in statistical mechanics and related fields.
Following a brief introductory chapter, the book explores statistical mechanics, the one-dimensional Ising model, dimer statistics, specific heat of Onsager's lattice in the absence of a magnetic field, boundary specific heat and magnetization, and boundary spin-spin correlation functions. Subsequent chapters cover the correlation functions, Wiener-Hopf sum equations, spontaneous magnetization, behavior of the correlation functions, asymptotic expansion, and boundary hysteresis and spin probability functions. Two other chapters examine Ising models with random impurities in terms of specific heat and boundary effects. The book concludes with a new chapter examining developments in the field since 1973.

Author Biography

Professor Barry M. McCoy is on the faculty of the C. N. Yang Institute for Theoretical Physics at Stony Brook University.

Tai Tsun Wu is Gordon McKay Professor of Applied Physics at Harvard University.

Table of Contents

Preface to Second Edition

Preface

I. Introduction

II. Statistical Mechanics

III. The One-Dimensional Ising Model

IV. Dimer Statistics

V. Specific Heat of Onsager's Lattice in the Absence of a Magnetic Field

VI. Boundary Specific Heat and Magnetization

VII. Boundary Spin-Spin Correlation Functions

VIII. The Correlation Functions

IX. Wiener-Hopf Sum Equations

X. Spontaneous Magnetization

XI. Behavior of the Correlation Functions

XII. Asymptotic Expansion

XIII. Boundary Hysteresis and Spin Probability Functions

XIV. An Ising Model with Random Impurities: Specific Heat

XV. An Ising Model with Random Impurities: Boundary Effects

XVI. Epilogue

XVII. Developments Since 1973

Appendix A

Appendix B

Index