The course provides an introduction to equilibrium statistical mechanics, both for classical and for quantum systems. In particular, the following topics will be covered:
- thermodynamic properties of interacting classical gases (van der Waals equation; perturbative methods and cluster expansions);
- phase transitions and Lee-Yang theorems;
- critical phenomena (Ginzburg-Landau theory, introduction to the renormalization group and universality);
- quantum statistics and noninteracting quantum gases (Bose-Einstein condensation; magnetic properties of free-fermion gases);
- second quantization and quantum many-body systems (weakly interacting Bose gases; fermionic systems on a lattice);
- quantum phase transitions (solution of the 1D quantum Ising model).