The course, worth 6 credits and comprising 24 lectures (2h each), is organised into two main parts:

1. Basic material
2. 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: 

Basic material:

• 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

Selected topics:

• The two-dimensional XY model
• Wegner's Ising lattice gauge theory. The Kitaev thoric code model. Brief intro to U(1) lattice gauge theory.