## Critical Phenomena and the Renormalisation Group

Ray Jones

**Introduction**: phenomenology, order parameters, critical temperatures and exponents.
- Magnetism as a paradigm: Ising and Heisenberg models and arguments about the possibility of a phase transition for d=1 and d=2. Spin waves. n and d.
**Fluctuations**: linear response theory, fluctuation dissipation theorem, correlation functions and \chi (**q**).
- Classical mean field theory applied to the Ising model and calculation of critical exponents: Ornstein -Zernicke theory and the role of the correlation length \xi (T). Failings of the theory and the Ginzburg criterion- the special role of d=4.
- Scaling: the static scaling hypothesis, exponent (in)equalities, Kadanoff block scaling.
- Introduction to the Wilson renormalisation group: role of fixed points and scale invariance, the correlation length exponent \nu and the linearised transformation.
- Approximate real space renormalisation group analysis of the Ising model when d=2.
- Universality.
- Percolation theory: an introduction to the ideas; calculation of
*p** and \nu by real space renormalisation group methods.
- Introduction to reciprocal space renormalisation group methods.
- The Kosterlitz-Thouless transition.

Bibliography