(Ebook) The two dimensional Ising model 2nd Edition by Barry M McCoy, Tai Tsun Wu ISBN 9780486493350 0486493350

(Ebook) The two dimensional Ising model 2nd Edition by Barry M McCoy, Tai Tsun Wu ISBN 9780486493350 0486493350

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Product details:

ISBN 10: 0486493350
ISBN 13: 9780486493350
Author: Barry M McCoy, Tai Tsun Wu

(Ebook) The two dimensional Ising model 2nd Edition Table of 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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