by
Giacomo Gradenigo
(Gran Sasso Science Institute)
→
Europe/Rome
Description
Abstract. This is an advanced course in statistical mechanics with the purpose of introducing the main ideas and tools to describe the low temperature phase of disordered systems, one among the topics for which a few years ago our Giorgio Parisi was awarded with the Nobel prize in physics. The main goal of this course is to explain the deep physical meaning of the replica-symmetry-breaking formalism and how it allows us to appropriately describe systems with a low temperature phase characterized by a very rugged free-energy landscape (many metastable minima). Assuming a basic knowledge of phase transitions in magnetic systems, I will present a detailed study (calculation of the free energy) of two prototypical models of disordered systems:
the Hopfield model (neural network),
the Sherrington-Kirkpatrick model (disordered mean-field Ising model).
References In attachment you can find useful notes for the models and calculations which will be presented during the course.
