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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 multi particle 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 2) are princi pally concerned with phase transitions in lattice systems. Due mainly to the insights gained from scaling theory and renormalization group methods, this 1 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 include some of our discussion of exact results in this volume and some in Volume 2. The other main area of discussion in this volume is mean-field theory leading to closed form approximations. Although this is known not to give reliable results close to a critical region, it often provides a good qualitative picture for phase dia grams as a whole. For complicated systems some kind of mean-field method is often the only tractable method available.
Sommario
1. Introduction to Thermodynamics and Phase Transitions.- 2. Statistical Mechanics and the One-Dimensional Ising Model.- 3. The Mean-Field Approximation, Scaling and Critical Exponents.- 4. Antiferromagnets and Other Magnetic Systems.- 5. Lattice Gases.- 6. Solid Mixtures and the Dilute Ising Model.- 7. Cluster Variation Methods.- 8. Exact Results for Two-Dimensional Ising Models.- 9. Applications of Transform Methods.- 10. The Six-Vertex Model.- A. Appendices.- A.1 Regular Lattices.- A.2 Elliptic Integrals and Functions.- A.2.1 Elliptic Integrals.- A.2.2 Elliptic Functions.- A.2.3 Results Required for Chapter 8.- A.3 The Water Molecule and Hydrogen Bonding.- A.4 Results for the Six-Vertex Model.- A.4.1 The Proof of I.- A.4.2 The Proof of II.- A.4.3 The Proof of III.- A.4.4 The Proof of IV.- A.5 Fourier Transforms and Series.- A.5.1 Fourier Transforms.- A.5.2 Fourier Series.- References and Author Index.
