Two-Dimensional Ising Model : Second Edition.

✍ Scribed by McCoy, Barry M.

• Publisher: Dover Publications
• Year: 2014
• Tongue: English
• Category: Library

✦ Synopsis

"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.  Read more...

✦ Table of Contents

Title
Copyright
Dedication
Preface to the Dover Edition
Preface
Contents
I Introduction
1 Introduction
2 The Ising Model
3 Literature
II Statistical Mechanics
1 Introduction
2 Microcanonical Ensemble
3 Canonical Ensemble
4 Thermodynamics
5 The Thermodynamic Limit
6 Extensions of Statistical Mechanics
III The One-Dimensional Ising Model
1 Introduction
2 Partition Function
3 Spin-Spin Correlation Functions
IV Dimer Statistics
1 Introduction
2 The Pfaffian
3 Dimer Configurations on Lattices with Free Boundary Conditions. 4 Dimer Configurations on Lattices with Cylindrical Boundary Conditions5 Dimer Configurations on Lattices with Toroidal Boundary Conditions
6 Evaluation of the Pfaffians
7 The Thermodynamic Limit
V Specific Heat of Onsager's Lattice in the Absence of a Magnetic Field
1 Introduction
2 The Partition Function for Onsager's Lattice
3 The Specific Heat of Onsager's Lattice
4 The Antiferromagnetic Seam
VI Boundary Specific Heat and Magnetization
1 Introduction
2 Formulation of the Problem
3 Partition Function
4 Boundary Free Energy and Specific Heat
5 Boundary Magnetization.

✦ Subjects

Ising model;SCIENCE -- Energy;SCIENCE -- Mechanics -- General;SCIENCE -- Physics -- General