Exactly Solved Models: A Journey in Statistical Mechanics

The following sections are included:

• Introduction by C.N. Yang

• Preface

• Contents

The following sections are included:

• Introduction

• The Pfaffian Approach

• The Rectangular Lattice

• Rectangular Lattice with a Boundary Vacancy

• The Honeycomb and Kagome Lattices

• Solution of a Three-Dimensional Dimer Model

• Remarks

• References for Chapter 1

The following sections are included:

• Introduction

• The Eight-Vertex Model (Rectangular Lattice)

• The Five-Vertex Model (Rectangular Lattice)

• The Eight-Vertex Model (Honeycomb Lattice)

• Vertex Models in Higher Dimensions

• Remarks

• References for Chapter 2

The following sections are included:

• Introduction

• Duality Relation for the Potts and the Chiral Potts Models

• Gauge Transformation for the Vertex Model and Syzygies

• Duality Relation for Frustrated Spin Systems

• Duality Relation for Potts Correlation Functions

• References for Chapter 3

The following sections are included:

• Introduction

• Ising Representation of the Eight-Vertex Model

• The Baxter-Wu Model

• Density of Fisher Zeroes

• Solution of the Ising Model on Nonorientable Surfaces

• Remarks

• References for Chapter 4

The following sections are included:

• Introduction

• Graphical Formulation of the Potts Model

• Rigorous Determination of the Potts Critical Point

• Potts Partition Function Zeroes

• Remarks

• References for Chapter 5

The following sections are included:

• Introduction

• The Potts Model

• The Antiferromagnetic Ising Model in a Magnetic Field

• The Blume-Emery-Griffiths Model

• The Ashkin-Teller Model

• The O(n) Model

• Remarks

• References for Chapter 6

The following sections are included:

• Introduction

• The Random-Cluster model and the Potts Model

• Percolation Thresholds

• An Infinite-Range Bond Percolation

• Directed Percolation

• Remarks

• References for Chapter 7

The following sections are included:

• Introduction

• Graphical Analyses in Many-Body Theory

• The Potts Model and the Tutte Polynomial

• Random Graphs

• Spanning Trees

• Graphical Analysis of Lattice Models

• References for Chapter 8

The following sections are included:

• Introduction

• Lattice Models and Knot Invariants

• Two New Knot Invariants

• Knot Invariants from Spin Models

• Bracket Polynomial and the Nonintersecting String Model

• Remarks

• References for Chapter 9

The following sections are included:

• Theory of Electric Circuits

• Quantization of the orbital angular momentum

• The Vicious Neighbor Problem

• Restricted Partitions of an Integer

• The Hubbard Model

• Review of a Book by Ta-You Wu

• Eulogy on Shang-Keng Ma

• Professor C. N. Yang and Statistical Mechanics

• References for Chapter 10

The following sections are included:

• PHOTOGRAPHS

This section consists of reprinted articles in the following topics:

• Dimer Statistics

• The Vertex Model

• Duality and Gauge Transformations

• The Ising Model

• The Potts Model

• Critical Frontiers

• Percolation

• Graph Theory

• Knot Invariants

• Other Topics

The following sections are included:

• APPENDIX
  • Research Summary

• Fa Yueh Wu: Vita

• Index of Names in the Commentaries