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

TL;DR

This paper explores how aging glassy systems respond to random perturbations, establishing a connection between their out-of-equilibrium dynamics and equilibrium properties, and proposing measurable order parameters to characterize their state organization.

Contribution

It introduces a new order parameter function linking response and fluctuation in aging systems and relates dynamic ultrametricity to static ultrametricity, aiding experimental analysis.

Findings

The free energy at long times equals equilibrium free energy.

The new order parameter function is related to the static overlap distribution.

Ultrametric organization in dynamics implies static ultrametricity.

Abstract

We discuss the response of aging systems with short-range interactions to a class of random perturbations. Although these systems are out of equilibrium, the limit value of the free energy at long times is equal to the equilibrium free energy. By exploiting this fact, we define a new order parameter function, and we relate it to the ratio between response and fluctuation, which is in principle measurable in an aging experiment. For a class of systems possessing stochastic stability, we show that this new order parameter function is intimately related to the static order parameter function, describing the distribution of overlaps between clustering states. The same method is applied to investigate the geometrical organization of pure states. We show that the ultrametric organization in the dynamics implies static ultrametricity, and we relate these properties to static separability, i.e., the property that the measure of the overlap between pure states is essentially unique. Our results, especially relevant for spin glasses, pave the way to an experimental determination of the order parameter function.