Renormalisation Group and Critical Phenomena

Prof. J. Cardy - Hilary Term 2005

The renormalisation group (RG) is both a conceptual and a computational basis for understanding many problems in physics and other sciences which exhibit the property of scale invariance or self-similarity. This is most clearly illustrated in materials, such as magnets or fluids, in the vicinity of a second-order phase transition.

This first-year graduate level course is intended to serve as an introduction to the ideas of the RG as applied to such systems. The lectures will largely be based on my book Scaling and Renormalization in Statistical Physics, 256 pp, ISBN 0521499593, CUP, 1996, for which only an undergraduate knowledge of statistical mechanics is required, but there will be additional material discussing the connection with the RG in quantum field theory, in which some of the material covered in the lectures Introduction to Quantum Field Theory (Michaelmas Term, 2004) will be assumed.

Topics to be covered include:

1. Phase transitions in simple systems
2. Mean field theory and its limitations
3. Basic theory of the RG
4. Scaling and crossover behaviour
5. Perturbative RG and the $\epsilon$-expansion
6. Relation to the field-theoretic RG
7. Some applications (depending on time):
   • low-dimensional systems
   • random magnets
   • polymer statistics
   • critical dynamics

The lectures will be on Thursdays and Fridays at 11 am in the Fisher Room, Denys Wilkinson Building.