The response of glassy systems to random perturbations: A bridge between equilibrium and off-equilibrium

Wt discuss the response of aging systems with short-range interactions to a class of random perturbations. Although these systems are out of equilibri um, the limit value of the free energy at long times is equal to the equili brium free energy. By exploiting this fact, we define a new order parameter function, and we relate it to the ratio between response and nuctuation, w hich is in principle measurable in an aging experiment. For a class of syst ems possessing stochastic stability, we show that this new order parameter function is intimately related to the static order parameter function, desc ribing the distribution of overlaps between clustering states. The same met hod is applied to investigate the geometrical organization of pure states. We show that the ultrametric organization in the dynamics implies static ul trametricity, and we relate these properties to static seperability, i.e., the property that the measure of the overlap between pure states is essenti ally unique. Our results, especially relevant for spin glasses, pave the wa y to an experimental determination of the order parameter function.