Events Archive

Véronique Gayrard:

Aging in mean field spin glasses

Abstract: I will review some of the main rigorous results on aging of activated dynamics of mean-field spin glasses obtained over the last decades, and discuss key technical aspects of the their proofs.

Jean-Christophe Mourrat:

On the free energy of mean-field spin glasses with multiple types

Abstract: Spin glasses are models of statistical mechanics in which a large number of elementary units interact with each other in a disordered manner. In the simplest case called the Sherrington-Kirkpatrick (SK) model, there are interactions between any two units in the system. We are mostly interested in a more general situation in which the units of the system can be decomposed into a finite number of types. For instance, one can think of a bipartite model in which the units are split into two groups, and the interactions only go from one group to the other one. Much useful information can be extracted from the analysis of the asymptotic behavior of the free energy of the system, in the limit of large system size. For models with a single type such as the SK model, we know how to represent this limit as a variational formula for a certain functional. However, this variational formula does not generalize well to models with multiple types such as the bipartite model. In this talk, I will explain that at least we can guarantee, for any model, that the limit free energy must be a critical value of the said functional.

Joint work with Hong-Bin Chen.