(Gran Sasso Science Institute)
Abstract: The course will be a short introduction to the main ideas and methods in the modern statistical mechanics of disordered systems. In particular we will discuss how the replica-symmetry-breaking formalism introduced by Paris is capable to efficiently describe ergodicity breaking in disordered systems.
The course will focus on the calculations of free energy in the mean-field approximation (exact in the large-N limit for the models considered) for two models: the Hopfield model for neural networks and the Sherrington-Kirkpatrick model (mean-field disordered Ising model). We will stress the meaning of the "matrix" order parameter which characterizes the glass transition and we will insist on the physical meaning and relevance of replica symmetry breaking.