Many systems display, under certain conditions, glassy behaviour. Our main objective is to better understand, at a theoretical level, what are the microscopic mechanisms leading to such a behaviour and how to describe them. In the case of Spin Glasses, where disorder is present in the Hamiltonian in the form of random couplings, mean-field models offer a privileged context where investigating glassy behaviour. Here, we have understood in great detail the structure of the energy landscape and how it is related to the non trivial thermodynamics and dynamics of the system. The Replica Theory provides a powerful approach to the complex low temperature phase of these systems, which is described in terms of a "Replica Symmetry Broken' solution (RSB). Recently we focused on a few models where the low temperature thermodynamical solution could be computed analytically, and where some kind of solutions never observed before were found for the first time. Similar techniques were also applied to a model interpolating between a standard laser (ordered) and a random laser (glassy), and to a random laser model both in presence and in absence of a saturable absorber. An important open issue is to understand whether the RSB scenario also holds beyond the mean-field approximation. In this context we focused on diluted models with power-law decaying interactions and showed evidence for the validity of the RSB theory. For what concerns finite dimentional systems, on the one hand we are contributing to further develop a Spin Glass field theory, on the other hand we are focusing on numerical simulations of several spin glass models. Contrary to spin glasses, structural glasses and supercooled liquids do not have quenched disorder in the Hamiltonian. Still, glassy behaviour is observed at low temperatures and the phenomenology much resembles the one of some mean-field spin glass models (p-spin models). For this reason, concepts and techniques from spin glasses have been widely applied to investigate glassy behaviour in these systems. In this context, we have recently investigated the limits and constraints of the concept of effective temperature, much used in spin glasses, as an off-equilibrium thermodynamic parameter for structural glasses. We have also developed some mean-field models apt to describe glasses with Johari-Goldstein processes and glass-to-glass transitions. Finally, we have developed new tecnhiques to detect the growth of amorphous order in supercooled liquids by using a smartly chosen, nonstandard order parameter, and we have interpreted our results in the context of the mosaic multi-state picture of the supercooled liquid phase.
This section is edited by Irene Giardina.