Scaling and Renormalization in Statistical Physics

A thoroughly modern graduate-level introduction to the theory of critical behaviour.

John Cardy (Author)

9780521499590, Cambridge University Press

Paperback, published 26 April 1996

260 pages, 49 b/w illus. 4 tables 63 music examples 63 exercises
23.2 x 15.1 x 1.7 cm, 0.4 kg

'Supported with interesting exercises at the end of each chapter, Cardy's book is likely to prove a popular introduction to this demanding but extraordinarily successful method for probing many complex phenomena.' Robert Matthews New Scientist

This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. Beginning with a brief review of phase transitions in simple systems and of mean field theory, the text then goes on to introduce the core ideas of the renormalization group. Following chapters cover phase diagrams, fixed points, cross-over behaviour, finite-size scaling, perturbative renormalization methods, low-dimensional systems, surface critical behaviour, random systems, percolation, polymer statistics, critical dynamics and conformal symmetry. The book closes with an appendix on Gaussian integration, a selected bibliography, and a detailed index. Many problems are included. The emphasis throughout is on providing an elementary and intuitive approach. In particular, the perturbative method introduced leads, among other applications, to a simple derivation of the epsilon expansion in which all the actual calculations (at least to lowest order) reduce to simple counting, avoiding the need for Feynman diagrams.

Preface
1. Phase transitions in simple systems
2. Mean field theory
3. The renormalization group idea
4. Phase diagrams and fixed points
5. The perturbative renormalization group
6. Near two dimensions
7. Surface critical behaviour
8. Random systems
9. Polymer statistics
10. Critical dynamics
11. Conformal symmetry
Appendix: Gaussian integration
Selected bibliography
Index.

Subject Areas: Statistical physics [PHS]