8.334: Statistical Physics of Fields

Spring 2024

NB. This outline is subject to change as term progresses.

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.

  • 8.334   Course Outline - last update    1/9/2024   by M. Kardar