A Method for Studying Model Hamiltonians
A Minimax Principle for Problems in Statistical Physics
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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.
Table of Contents
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
§ 9. The Question of the Choice of Sign for the Source-Terms
§ 10. The Construction of Upper-Bound Inequalities in the Case When C=0
Chapter 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 Principle
References
Index
Product details
- No. of pages: 180
- Language: English
- Copyright: © Pergamon 1972
- Published: January 1, 1972
- Imprint: Pergamon
- eBook ISBN: 9781483148779
About the Author
N. N. Bogolyubov
About the Editor
D. ter Haar
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