Statistical Mechanics

1. Front Matter

   Pages I-IX

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2. Commentaries

   1. Front Matter

      Pages 1-1

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   2. A Survey by the Editors

      • Bruno Nachtergaele, Jan Philip Solovej, Jakob Yngvason

      Pages 3-10

3. Thermodynamic Limit for Coulomb Systems

   1. Front Matter

      Pages 11-11

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   2. Existence of Thermodynamics for Real Matter with Coulomb Forces

      • J. L. Lebowitz, Elliott H. Lieb

      Pages 13-16

   3. The Constitution of Matter: Existence of Thermodynamics for Systems Composed of Electrons and Nuclei

      • Elliott H. Lieb, Joel L. Lebowitz

      Pages 17-24

4. Hard Sphere Virial Coefficients

   1. Front Matter

      Pages 25-25

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   2. Suppression at High Temperature of Effects Due to Statistics in the Second Virial Coefficient of a Real Gas

      • Sigurd Yves Larsen, John E. Kilpatrick, Elliot H. Lieb, Harry F. Jordan

      Pages 27-28

   3. Calculation of Exchange Second Virial Coefficient of a Hard-Sphere Gas by Path Integrals

      • Elliott H. Lieb

      Pages 29-38

5. Zeros of Partition Functions

   1. Front Matter

      Pages 39-39

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   2. Monomers and Dimers

      • Ole J. Heilmann, Elliott H. Lieb

      Pages 41-43

   3. Theory of Monomer-Dimer Systems

      • Ole J. Heilmann, Elliott H. Lieb

      Pages 45-87

   4. A Property of Zeros of the Partition Function for Ising Spin Systems

      • Elliott H. Lieb, David Ruelle

      Pages 89-92

   5. A General Lee—Yang Theorem for One-Component and Multicomponent Ferromagnets

      • Elliott H. Lieb, Alan D. Sokal

      Pages 93-119

6. Reflection Positivity

   1. Front Matter

      Pages 121-121

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   2. Existence of Phase Transitions for Anisotropic Heisenberg Models

      • Jürg Fröhlich, Elliott H. Lieb

      Pages 123-125

   3. Phase Transitions in Anisotropic Lattice Spin Systems

      • Jürg Fröhlich, Elliott H. Lieb

      Pages 127-161

   4. Phase Transitions in Quantum Spin Systems with Isotropic and Nonisotropic Interactions

      • Freeman J. Dyson, Elliott H. Lieb, Barry Simon

      Pages 163-211

   5. Phase Transitions and Reflection Positivity. I. General Theory and Long Range Lattice Models

      • Jürg Fröhlich, Robert Israel, Elliot H. Lieb, Barry Simon

      Pages 213-246

   6. Phase Transitions and Reflection Positivity. II. Lattice Systems with Short-Range and Coulomb Interactions

      • Jürg Fröhlich, Robert B. Israel, Elliott H. Lieb, Barry Simon

      Pages 247-297

In Statistical Physics one of the ambitious goals is to derive rigorously, from statistical mechanics, the thermodynamic properties of models with realistic forces. Elliott Lieb is a mathematical physicist who meets the challenge of statistical mechanics head on, taking nothing for granted and not being content until the purported consequences have been shown, by rigorous analysis, to follow from the premises. The present volume contains a selection of his contributions to the field, in particular papers dealing with general properties of Coulomb systems, phase transitions in systems with a continuous symmetry, lattice crystals, and entropy inequalities. It also includes work on classical thermodynamics, a discipline that, despite many claims to the contrary, is logically independent of statistical mechanics and deserves a rigorous and unambiguous foundation of its own. The articles in this volume have been carefully annotated by the editors.

• Coulomb Systems
• Lattice Crystals
• Statistical Mechanics
• entropy
• phase Transition
• statistical physics
• thermodynamics

• Department of Mathematics, University of California, Davis, USA

  Bruno Nachtergaele

• Department of Mathematics, University of Copenhagen, Copenhagen, Denmark

  Jan Philip Solovej

• Institut für Theoretische Physik, Universität Wien, Wien, Austria

  Jakob Yngvason

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