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Statistical Mechanics

Selecta of Elliott H. Lieb

  • Book
  • © 2004

Overview

Editors:
  1. Bruno Nachtergaele

    1. Department of Mathematics, University of California, Davis, USA

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  2. Jan Philip Solovej

    1. Department of Mathematics, University of Copenhagen, Copenhagen, Denmark

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  3. Jakob Yngvason

    1. Institut für Theoretische Physik, Universität Wien, Wien, Austria

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  • The papers collected in this volume written by one of the leading mathematical physicists are considered as outstanding accomplishments in statistical mechanics research.

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Table of contents (28 chapters)

  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
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Keywords

About this book

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.

Editors and Affiliations

  • 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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