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 PrefacePrefaceIntroduction
1. General Remarks
2. Remarks an Quasi-AveragesChapter 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 AveragesChapter 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 LimitsChapter 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 ¿ of the Free Energy Function and on Bounds for the Quantities dv
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
9. The Question of the Choice of Sign for the Source-Terms
10. The Construction of Upper-Bound Inequalities in the Case When C=0Chapter 4. Model Systems with Positive and Negative Interaction Components
1. Hamiltonian with Negative Coupling Constants (Repulsive Interaction)
2. Features of the Asymptotic Relations for the Free Energies in the Case of Systems with Positive Interaction
3. Bounds for the Free Energies and Correlation Functions
4. Examination of an Auxiliary Problem
5. Solution of the Question of Uniqueness
6. Hamiltonians with Coupling Constants of Different Signs. The Minimax PrincipleReferencesIndex