Statistical Mechanics of Lattice Systems

1. Front Matter

   Pages I-XII

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2. Thermodynamics and Statistical Mechanics

   • David A. Lavis, George M. Bell

   Pages 1-14

3. Phase Transitions and Scaling Theory

   • David A. Lavis, George M. Bell

   Pages 15-87

4. Landau and Landau-Ginzburg Theory

   • David A. Lavis, George M. Bell

   Pages 89-112

5. Algebraic Methods in Statistical Mechanics

   • David A. Lavis, George M. Bell

   Pages 113-165

6. The Eight-Vertex Model

   • David A. Lavis, George M. Bell

   Pages 167-202

7. Real-Space Renormalization Group Theory

   • David A. Lavis, George M. Bell

   Pages 203-249

8. Series Methods

   • David A. Lavis, George M. Bell

   Pages 251-302

9. Dimer Assemblies

   • David A. Lavis, George M. Bell

   Pages 303-333

10. Back Matter

    Pages 335-431

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Most of the interesting and difficult problems in statistical mechanics arise when the constituent particles of the system interact with each other with pair or multipartiele energies. The types of behaviour which occur in systems because of these interactions are referred to as cooperative phenomena giving rise in many cases to phase transitions. This book and its companion volume (Lavis and Bell 1999, referred to in the text simply as Volume 1) are princi­ pally concerned with phase transitions in lattice systems. Due mainly to the insights gained from scaling theory and renormalization group methods, this subject has developed very rapidly over the last thirty years. ' In our choice of topics we have tried to present a good range of fundamental theory and of applications, some of which reflect our own interests. A broad division of material can be made between exact results and ap­ proximation methods. We have found it appropriate to inelude some of our discussion of exact results in this volume and some in Volume 1. Apart from this much of the discussion in Volume 1 is concerned with mean-field theory. Although this is known not to give reliable results elose to a critical region, it often provides a good qualitative picture for phase diagrams as a whole. For complicated systems some kind of mean-field method is often the only tractable method available. In this volume our main concern is with scaling theory, algebraic methods and the renormalization group.

• Phase transition
• Renormalization group
• STEM
• cluster variation method
• mean-field approximation
• renormalization method
• scaling

• Department of Mathematics, King’s College, University of London Strand, London, UK

  David A. Lavis, George M. Bell

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