Chapter 12. Mean-Field Theory III: Landau Formulation

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

Published Online: 28 JAN 2005

DOI: 10.1002/3527603158.ch12

Principles of Equilibrium Statistical Mechanics

Principles of Equilibrium Statistical Mechanics

How to Cite

Chowdhury, D. and Stauffer, D. (2000) Mean-Field Theory III: Landau Formulation, in Principles of Equilibrium Statistical Mechanics, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527603158.ch12

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;
  • mean-field theory;
  • Landau formulation;
  • second order phase transition;
  • first order phase transitions;
  • Landau-Ginzburg theory;
  • two-point correlation function;
  • Ginzburg criterion

Summary

This chapter contains sections titled:

  • Introduction

  • Second Order Phase Transitions

    • Critical Exponents in Landau Theory

  • First Order Phase Transitions

    • Field-driven Transition

    • T-driven Transition; Asymmetric Case

    • T-driven Transition; Symmetric Case

  • Landau-Ginzburg Theory

  • Two-Point Correlation Function

    • Fourier Transform Method

    • Method of Solving Differential Equation

  • Ginzburg Criterion

  • Chapter Summary

  • Historical Notes

  • Problems

  • Supplementary Notes

    • Landau theory for Tricritical Points

    • Gaussian Fluctuations and Ginzburg Criterion

    • “Derivation” of Landau-Ginzburg Effective Hamiltonian