The course, worth 6 credits and comprising 24 lectures (2h each), is organised into two main parts:
- Basic material
- Selected topics
The basic material contains standard topics. Starting with a review of thermodynamics, the statistical ensembles are introduced, and standard applications (systems of free bosons and fermions) are illustrated. Next, after an interlude on transfer matrix and path-integral representation, the standard Weiss mean-field theory approach is presented, ending with a derivation of the Ginzburg-Landau action.
The selected topics include, this year: an introduction to the classical XY model in two dimensions and to the Kosterlitz-Thouless transition, and an introduction to Ising lattice gauge theory and beyond.
A more detailed syllabus would be:
- Introduction to entropy and statistical mechanics
- Review of thermodynamics
- Statistical mechanics ensembles: microcanonical, canonical, and grandcanonical
- Applications to free gases and waves.
- Quantum statistical mechanics of harmonic oscillators, and of ideal Fermi and Bose gases.
- Sommerfeld low-T expansion for Fermi systems; Bose-Einstein condensation.
- Phase transitions, universality and critical phenomena (brief overview)
- Transfer matrix method and quantum-classical correspondence
- Mean Field Theory
- Landau-Ginzburg action: from the Ising model to the φ4 field-theory
- The two-dimensional XY model
- Wegner's Ising lattice gauge theory. The Kitaev thoric code model. Brief intro to U(1) lattice gauge theory.