Disorder And Competition In Soluble Lattice Models : Advances in Statistical Mechanics - Walter F. Wreszinski

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Disorder And Competition In Soluble Lattice Models

By: Walter F. Wreszinski, Silvio R.A. Salinas

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Hardcover | 1 August 1993

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Hardcover
248 Pages

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22.56 x 16.15 x 1.83

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This book considers some exactly soluble lattice models in order to discuss modern methods and concepts in statistical mechanics. The authors use ideas from the theory of dynamical systems, general methods of statistical physics (thermodynamic limit, convexity and algebraic properties) and quantum mechanical techniques (Bethe Ansatz, conformal invariance, Perron-Frobenius theorem). The behaviour of systems are illustrated as dilute antiferromagnets, spin glasses, and modulated magnets and alloys. Specific examples are included to discuss the most important concepts (as disorder or frustration). Some simple lattice models are shown to give rise to spectacular phase diagrams, with multicritical points and sequences of modulated phases. A number of exercises are included to help the comprehension of the most representative issues. This book may be useful to graduate students in many areas of theoretical physics (condensed matter, field theory, mathematical physics).

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General Introduction	p. 1
Diluted Systems	p. 7
Annealed Models	p. 9
Mean-Field Ising Model in a Random Field	p. 15
The Hierarchical Random-Field Ising Model	p. 21
Griffiths Singularities in a Field	p. 31
Symmetry-Breaking and the Spherical Model in a Random Field	p. 35
Lattice Models with Competing Interactions	p. 41
Introduction. One-Dimensional Spin Models	p. 41
The Bak - Bruinsma - Aubry Model	p. 47
Aubry's Treatment of the Bak- Bruinsma- Aubry Model	p. 54
Linear Chain of Coupled Atoms and Dynamical Systems	p. 62
The Mean-Field ANNNI Model as an Area-Preserving Map	p. 69
Ising Models as a Mapping Problem on the Cayley Tree	p. 74
Spin Glasses	p. 93
Spin Glasses. Some General Aspects	p. 94
The Thermodynamic Limit after van Enter and van Hemmen	p. 98
The Replica Method of Hemmen and Palmer	p. 102
The Negative Entropy Problem	p. 109
Spin-Glass Models on a Cayley Tree	p. 111
Spin-Glass on a Cayley Tree at T = 0	p. 114
Spin-Glass on a Cayley Tree of Infinite Coordination	p. 120
Random Versus Nonrandom	p. 123
Quantum Lattice Models with Competing Interactions	p. 131
The Hubbard Model	p. 132
The RVB State	p. 140
Quantum Spin Chains with Competing Interaction	p. 143
Models of Localization	p. 159
Lifshitz Tails in Quantum Disordered Systems	p. 167
A: A Brief Introduction to Dynamical Systems	p. 177
Stability of Equilibrium Points	p. 179
Attractors and Strange Attractors	p. 182
The Kaplan-Yorke Attractor	p. 185
Fractal Dimension	p. 190
Bifurcations	p. 193
Area-Preserving Maps	p. 194
B: The Theorems of Aubry	p. 199
C: Bethe Ansatz and Conformal Invariance	p. 205
The Bethe Ansatz	p. 206
Some Aspects of Conformal Invariance	p. 214
D: Unicity of Phases, Unicity in a Sector, and Spontaneous Symmetry Breaking	p. 223
Subject Index	p. 231
Author Index	p. 233
Table of Contents provided by Blackwell. All Rights Reserved.

Disorder And Competition In Soluble Lattice Models

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