The Statistical Mechanics of Lattice Gases vol.1

Description

Title page INTRODUCTION I. Preliminaries 1. Models to be Discussed Appendix to 1.1. Thermodynamics and the Models of Statistical Mechanics 2. Models Not to be Discussed 3. Convexity Inequalities: Abelian Case 4. Convexity Inequalities: Non-Abelian Case 5. Linear Functionals on Infinite-Dimensional Spaces 6. Legendre Transforms 7. States on C*-Algebras II. The Pressure 1. The Basic Formalism 2. Convergence of the Pressure: Free Boundary Conditions 3. Convergence of the Pressure: Other Boundary Conditions 4. Pressure for Coulomb Interactions 5. Transfer Matrices, I: One Dimension 6. Transfer Matrices, II: Two-Dimensional Ising Model 7. Duality and Other Transformations Appendix to II.7. Bethe Lattices and the Bethe Approximation 8. Surface Pressure and Surface Tension 9. Limit Theorem, I: Bishop-de Leeuw Order 10. Limit Theorems, II: Lieb's Method 11. Limit Theorems, III: llD Expansion 12. Ursell Functions 13. Mean Field Theory 14. Limit Theorems, IV: Mean Field Limit 15. Limit Theorems, V: Potts Model Limit III. States: The Classical Case 1. States 2. Equilibrium States: The DLR Equations 3. Translation Invariant Equilibrium States and Tangent Functionals 4. Entropy and the Gibbs Variational Principle Appendix to IIIA. The Microcanonical Ensemble 5. Pure States and Pure Phases 6. Ward Identities and the Classical Bogoliubov Inequalities 7. Absence of Continuous Symmetry Breaking in Two Dimensions 8. Energy Shift Estimates 9. The Third Law of Thermodynamics 10. Phase Transitions and Fluctuations of Macroscopic Observables 11. Decay of Correlations in Two-Dimensional Plane Rotors IV. States: The Quantum Case 1. States 2. Entropy and the Gibbs Variational Principle 3. Time Automorphisms 4. Equilibrium States: The KMS Condition 5. Equilibrium States: The Gibbs Condition Appendix to IV.5. KMS Conditions and the Second Law of Thermodynamics 6. Energy Shift Estimates 7. The Inequalities of Bogoliubov and Bruch-Falk 8. Absence of Continuous Symmetry Breaking in Two Dimensions V. High Temperature and Low Densities 1. Dobrushin's Uniqueness Theorem 2. Analyticity and Decay of Correlations 3. KRVO Distance and Mean Field Theory Bounds on Transition Temperatures 4. Ward Identities and Mean Field Theory Bounds on Transition Temperatures 5. Mean Field Bounds on the Magnetization 6. Fisher's Bounds 7. High-Temperature and Small-Fugacity Expansions Appendix to V.7. Combinatorial Aspects of Polymer Expansions 8. Low-Temperature Expansions 9. Detailed Analysis of the Decay of Correlations at Large Temperatures REFERENCES INDEX