Frontmatter -- CONTENTS -- INTRODUCTION. Convexity and the Notion of Equilibrium State in Thermodynamics and Statistical Mechanics -- I. Interactions -- II. Tangent Functionals and the Variational Principle -- III. DLR Equations and KMS Conditions -- IV. Decomposition of States -- V. Approximation by Tangent Functionals: Existence of Phase Transitions -- VI. The Gibbs Phase Rule -- APPENDIX [Alpha]. Hausdorff Measure and Dimension -- APPENDIX B. Classical Hard-Core Continuous Systems -- BIBLIOGRAPHY -- INDEX -- Backmatter
Summary
In this book, Robert Israel considers classical and quantum lattice systems in terms of equilibrium statistical mechanics. He is especially concerned with the characterization of translation-invariant equilibrium states by a variational principle and the use of convexity in studying these states. Arthur Wightman's Introduction gives a general and historical perspective on convexity in statistical mechanics and thermodynamics. Professor Israel then reviews the general framework of the theory of lattice gases. In addition to presenting new and more direct proofs of some known results, he uses
