A Method for Studying Model Hamiltonians

A Method for Studying Model Hamiltonians: A Minimax Principle for Problems in Statistical Physics centers on methods for solving certain problems in statistical physics which contain four-fermion interaction. Organized into four chapters, this book begins with a presentation of the proof of the asymptotic relations for the many-time correlation functions. Chapter 2 details the construction of a proof of the generalized asymptotic relations for the many-time correlation averages. Chapter 3 explains the correlation functions for systems with four-fermion negative interaction. The last chapter shows the model systems with positive and negative interaction components.

Series Editor's Preface Preface Introduction § 1. General Remarks § 2. Remarks an Quasi-Averages Chapter 1. Proof of the Asymptotic Relations for the Many-Time Correlation Functions § 1. General Treatment of the Problem. Some Preliminary Results and Formulation of the Problem § 2. Equations of Motion and Auxiliary Operator Inequalities § 3. Additional Inequalities § 4. Bounds for the Difference of the Single-Time Averages § 5. Remark (I) § 6. Proof of the Closeness of Averages Constructed on the Basis of Model and Trial Hamiltonians for "Normal" Ordering of the Operators in the Averages § 7. Proof of the Closeness of the Averages for Arbitrary Ordering of the Operators in the Averages Remark (II) § 8. Estimates of the Asymptotic Closeness of the Many-Time Correlation Averages Chapter 2. Construction of a Proof of the Generalized Asymptotic Relations for the Many-Time Correlation Averages § 1. Selection Rules and Calculation of the Averages § 2. Generalized Convergence § 3. Remark § 4. Proof of the Asymptotic Relations § 5. Remark on the Construction of Uniform Bounds § 6. Generalized Asymptotic Relations for the Green's Functions § 7. The Existence of Generalized Limits Chapter 3. Correlation Functions for Systems with Four-Fermion Negative Interaction § 1. Calculation of the Free Energy for Model Systems with Attraction § 2. Further Properties of the Expressions for the Free Energy § 3. Construction of Asymptotic Relations for the Free Energy § 4. On the Uniform Convergence with Respect to θ of the Free Energy Function and on Bounds for the Quantities δv § 5. Properties of Partial Derivatives of the Free Energy Function. Theorem 3.III § 6. Rider to Theorem 3.III and Construction of an Auxiliary Inequality § 7. On the Difficulties of Introducing Quasi-Averages § 8. A New Method of Introducing Quasi-Averages