Thermal Avalanches Drive Logarithmic Creep in Disordered Media

Disordered materials under an imposed forcing can display creep and aging effects, accompanied by intermittent, spatially heterogeneous dynamics. We propose a testable microscopic description of these phenomena, based on the notion that as the system ages, the density of local barriers that enable relaxation displays a slowly evolving gap. As a result, the relaxation dynamics is dominated by the activation of the lowest, extremal tail of the distribution. This framework predicts logarithmic creep, as well as correlated bursts of slow activated rearrangements, or "thermal avalanches," whose size grows logarithmically with their duration. The time interval between events within avalanches obeys a universal power-law distribution, with a cutoff that is simply proportional to the age of the system. We show that these predictions hold both in numerical models of amorphous solids, as well as in experiments with thin crumpled sheets. This analysis suggests that the heterogeneous dynamics occurring during logarithmic creep is related to other phenomena, including dynamical heterogeneities characterizing the glass transition.