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Index
Cover
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 Conditions
5 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
VII Boundary Spin-Spin Correlation Functions
1 Introduction
2 Formulation of the Problem
3 The Inverse of A
4 General Considerations
5 T > TC, N|1 − T/Tc| » 1
6 T < TC, E1> 0, N[1 − T/Tc] » 1
7 T < TC, E1 < 0
8 T Near Tc
VIII The Correlation Functions 〈σ0,0σ0,N〉 and 〈σ0,0σN,N〉
1 Introduction
2 〈σ0,0σ0,N〉 in Terms of an N × N Toeplitz Determinant
3 〈σ0,0σN,N〉 in Terms of an N × N Toeplitz Determinant
4 The Near-Neighbor Correlation Functions 〈σ0,0σ0,1〉 and 〈σ0,0σ1,1〉
IX Wiener-Hopf Sum Equations
1 Introduction
2 Mathematical Technicalities
3 Factorization
4 Ind C(ξ) = 0
5 Ind C(ξ) < 0
6 Ind C(ξ) > 0
X Spontaneous Magnetization
1 Introduction
2 Discovering Szegö’s Theorem
3 A Rigorous Proof of Szegö’s Theorem
4 Explicit Calculation of the Spontaneous Magnetization
XI Behavior of the Correlation Functions 〈σ0,0σ0,N〉 and 〈σ0,0σN,N〉 for Large N
1 Introduction
2 Spin Correlations Above the Critical Temperature
3 Spin Correlations Below the Critical Temperature
4 〈σ0,0σN,N〉 at T = Tc
5 〈σ0,0σ0,N〉 at T = Tc; Leading Term
6 〈σ0,0σ0,N〉 at T = Tc; Higher-Order Terms (I)
7 〈σ0,0σ0,N〉 at T = Tc; Higher-Order Terms (II)
XII Asymptotic Expansion of 〈σ0,0σM,N〉
1 Introduction
2 The Correlation 〈σ0,0σM,N〉
3 Spin Correlations Below the Critical Temperature
4 Spin Correlations Above the Critical Temperature
5 Discussion
XIII Boundary Hysteresis and Spin Probability Functions
1 Introduction
2 Boundary Hysteresis: A Crude Interpretation
3 Critical Isotherm
4 Boundary Hysteresis: A Refined Interpretation
5 Misfit Bond
XIV An Ising Model with Random Impurities: Specific Heat
1 Introduction
2 Formulation of the Problem
3 Integral equation for v(x)
4 Power-Law Distribution
5 Discussion
XV An Ising Model with Random Impurities: Boundary Effects
1 Introduction
2 Average Boundary Magnetization
3 Average Spin-Spin Correlation Functions
XVI Epilogue
XVII Developments Since 1973
1 Introduction
2 Scaling Theory
3 Expansion of Correlation Functions
4 Painlevé Equations
5 Nonlinear Partial Difference Equations
6 The Magnetic Susceptibility
7 The Ising Model for H ≠ 0
Appendix A
Appendix B
Index
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