Activation and Avalanche Length Scales in the Finite-Temperature Creep of an Elastic Interface

Abstract

We investigate the creep dynamics of a driven elastic line at finite temperature, well below the depinning threshold. We show that creep is governed by two distinct length scales. The first, ${\ell }_{\mathrm{opt}}$, corresponds to the optimal activated rearrangements that control the dynamics' bottleneck and remains essentially temperature-independent. The second, ${\ell }_{\mathrm{av}}$, characterizes the spatial extent of thermally activated avalanches and grows as temperature decreases. By combining structural and dynamical observables, we show that ${\ell }_{\mathrm{av}}$ governs both the crossover in the structure factor and the growth of the four-point dynamical susceptibility, while the relaxation time remains controlled by activation over large barriers associated with ${\ell }_{\mathrm{opt}}$. We find that the avalanche scale follows ${\ell }_{\mathrm{av}}(T)\sim T^{-{\nu }_{\mathrm{dep}}}$, thereby selecting a unique scenario among competing theoretical predictions. These results establish a unified picture of finite-temperature creep in which activation controls temporal scales while depinning criticality governs spatial correlations.

7 pages, 5 figures