Statistical Mechanics
Basic Course given by Giuseppe Santoro
Start Date
Mon: 14:00-16:00
Wed: 9:00-11:00
Fri: 11:00-13:00


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.  


Online resources

Filename Size Date Modified
Lecture notes 12.06 MB Thu, 01/11/2024 - 16:47