## 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:

- Phase transitions in simple systems
- Mean field theory and its limitations
- Basic theory of the RG
- Scaling and crossover behaviour
- Perturbative RG and the $\epsilon$-expansion
- Relation to the field-theoretic RG
- 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.