Chapter 7. Interacting Systems; Thermodynamic Limit

  1. Prof. Dr. Debashish Chowdhury1 and
  2. Prof. Dr. Dietrich Stauffer2

Published Online: 28 JAN 2005

DOI: 10.1002/3527603158.ch7

Principles of Equilibrium Statistical Mechanics

Principles of Equilibrium Statistical Mechanics

How to Cite

Chowdhury, D. and Stauffer, D. (2000) Interacting Systems; Thermodynamic Limit, in Principles of Equilibrium Statistical Mechanics, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527603158.ch7

Author Information

  1. 1

    Indian Institute of Technology, Kanpur, India

  2. 2

    University of Cologne, Germany

Publication History

  1. Published Online: 28 JAN 2005
  2. Published Print: 27 JUL 2000

ISBN Information

Print ISBN: 9783527403004

Online ISBN: 9783527603152

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Keywords:

  • statistical mechanics;
  • interacting systems;
  • thermodynamic limit;
  • models of fluids;
  • lattices;
  • spin models on lattices;
  • zeroes of the grand partition function;
  • use of the techniques of calculation

Summary

This chapter contains sections titled:

  • Introduction

  • Models of Fluids

    • Partition Function

  • Lattices

    • Bravais Lattices

    • Bethe Lattice

  • Spin Models on Lattices

    • Classical Spin-1/2 Ising Model

    • Spin-1/2 Ising Model: Physical Realizations

    • Generalization: From Spin-1/2 to Spin-1 Ising Model

    • Generalization: From Ising to Vector Spins

    • Generalization: From Ising to Potts Variables

    • Quantum Spin Models

    • Classical Limit of Quantum Spin Models

    • Magnetic Physical Realizations of Spin Models

  • Restrictions on the Interactions

  • Zeroes of the Grand Partition Function

    • Yang-Lee Theorems and Their Consequences

  • Chapter Summary

  • Historical Notes

    • Spin Models and Their Physical Realizations

    • Thermodynamic Limit

    • Yang-Lee Theorem

  • Problems

  • Supplementary notes

    • Continuum Models of Fluids

    • Spin Models on Discrete Lattices

    • Vertex Models

    • Generalization: From “Hard” Spins to “Soft” Spins

    • Spin Models with Quenched Disorder

    • Anisotropic Hamiltonians for Spin System

    • Thermodynamic Limit

    • Complex Temperature Plane: Zeroes of Partition Function

    • Quantum Phase Transitions and Critical Phenomena