Mean field glassy system have been the subject of much studies over the last decades. They arise as mean field models for the glass transition, but also as models for complex systems and optimization problems. Their thermodynamics properties can be solve using the replica, or the cavity method.

In this talk, I will introduce a generalization of the cavity method that allows to follow Gibbs states in mean field systems when an external parameter, e.g. the temperature, is tuned. The method thus yields a "static" way to study long time "dynamics" in mean field models of glass formers, spin glasses, or random constraint satisfaction problems. In optimization problems the method gives limits for the performance of the simulated annealing algorithm. It also gives new results on the stability and the marginality of the non-equilibrium states, on the spinodal point upon heating, and allow to demonstrate the presence of temperature chaos.

Reference : Krzakala, Zdeborova ; arXiv:0909.3820v1.

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