Statistical Mechanics of Lattice Systems: Volume 2: Exact, Series and Renormalization Group Methods

ISBN-13: 9783642084102 / Angielski / Miękka / 2010 / 430 str.

David A. Lavis; George M. Bell

Opis

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.

Spis treści

1. Thermodynamics and Statistical Mechanics.- 2. Phase Transitions and Scaling Theory.- 3. Landau and Landau-Ginzburg Theory.- 4. Algebraic Methods in Statistical Mechanics.- 5. The Eight-Vertex Model.- 6. Real-Space Renormalization Group Theory.- 7. Series Methods.- 8. Dimer Assemblies.- A. Appendices.- References and Author Index.

Blurb

This two-volume work provides a comprehensive study of the statistical mechanics of lattice models. It introduces the reader to the main areas in statistical mechanics and the theory of phase transitions. The development is built on a firm mathematical and physical basis. Volume 1 contains an account of mean-field and cluster variation methods successfully used in many applications in solid-state physics and theoretical chemistry as well as an account of exact results for the Ising and six-vertex models and those derivable by transformation methods. Volume 2 includes extensive treatments of scaling theory, algebraic and real-space group renormalization methods and the eight-vertex model. It also includes an account of series methods and a treatment of dimer assemblies.