Convexity in the theory of lattice gases
著者
書誌事項
Convexity in the theory of lattice gases
（Princeton legacy library）
Princeton University Press, [2015], c1979
- : pbk
- タイトル別名
-
Princeton series in physics
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注記
Reprint. Originally published: Princeton University Press, 1979
Originally series title: Princeton series in physics
Includes bibliographical references (p. 163-165) and index
内容説明・目次
内容説明
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 a version of a theorem by Bishop and Phelps to obtain existence results for phase transitions. Furthermore, he shows how the Gibbs Phase Rule and the existence of a wide variety of phase transitions follow from the general framework and the theory of convex functions. While the behavior of some of these phase transitions is very "pathological," others exhibit more "reasonable" behavior. As an example, the author considers the isotropic Heisenberg model.
Formulating a version of the Gibbs Phase Rule using Hausdorff dimension, he shows that the finite dimensional subspaces satisfying this phase rule are generic. Originally published in 1979. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
目次
*Frontmatter, pg. i*CONTENTS, pg. vii*INTRODUCTION. Convexity and the Notion of Equilibrium State in Thermodynamics and Statistical Mechanics, pg. ix*I. Interactions, pg. 1*II. Tangent Functionals and the Variational Principle, pg. 32*III. DLR Equations and KMS Conditions, pg. 55*IV. Decomposition of States, pg. 83*V. Approximation by Tangent Functionals: Existence of Phase Transitions, pg. 112*VI. The Gibbs Phase Rule, pg. 130*APPENDIX ALPHA. Hausdorff Measure and Dimension, pg. 143*APPENDIX B. Classical Hard-Core Continuous Systems, pg. 153*BIBLIOGRAPHY, pg. 163*INDEX, pg. 166
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