WP2 Mathematical Statistical Mechanics (K3)
The module covers the following topics: Gibbs measures: DLR conditions, existence, uniqueness (Dobrushin's theorem), phase transitions, absence of spontaneous symmetry breaking in two dimensions. Ising model: high temperature phase, Peierls argument, cluster expansion, Fortuin-Kasteleyn representation, FKG inequality, spontaneous symmetry breaking in continuous models. Non-equilibrium model systems: Exclusion processes, matrix product ansatz, interacting particle systems. The main goal of this module is to acquire a deeper mathematical and physical understanding of phase transitions and collective phenomena that occur in macroscopic interacting particle systems.