Tentative outline
1. Collective modes: Hydrodynamic
limit; Importance of symmetries and dimensionality. Introduction to phase
transitions and critical phenomena.
2. The Landau-Ginzburg model: Mean-Field Theory;
Critical exponents; Goldstone modes and the Lower critical dimension; Fluctuations
and the Upper critical dimension.
3. Universality: Self-similarity; the Scaling
hypothesis; Kadanoff's heuristic Renormalization Group (RG), and exponent
identities.
4. Perturbation theory: Diagrammatic expansions;
Wilson's momentum space RG, and the taming of divergent perturbation series
by epsilon-expansions.
5. Lattice models: Ising, Potts, etc.; Position-space
RGs (cumulant, Migdal-Kadanoff); Monte-Carlo simulations; Finite-size scaling.
6. Series expansions: Low temperatures and
High temperatures; Duality; Random walk generating functions; Exact solution
of the two-dimensional Ising model.
7. Two-dimensional films: Algebraic order;
Topological defects; Melting and the Hexatic phase; the non-linear sigma model.
(If time permits, one of the following topics:)
8. Dynamics: Langevin equations; Conservation
laws; Dynamic universality classes.
9. Random systems: Annealed versus Quenched
impurities; Harris' Criterion; Random bonds; Random fields; Spin-glasses.
10. Scaling theories of Polymers, and other networks.