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

TL;DR

This paper studies the creep behavior of an elastic interface at finite temperature, revealing two key length scales that govern dynamics and spatial correlations, and clarifying their roles in the creep process.

Contribution

It identifies and characterizes two distinct length scales, $\, ext{ extltilde} ext{ extltilde}_{ ext{opt}}$ and $\, ext{ extltilde} ext{ extltilde}_{ ext{av}}$, in finite-temperature creep, linking them to structural and dynamical observables.

Findings

The avalanche length scale $\, ext{ extltilde} ext{ extltilde}_{ ext{av}}$ grows as temperature decreases, following a power law.

The relaxation time is controlled by activation over barriers related to $\, extltilde}_{ ext{opt}}$.

The results unify activation-controlled temporal scales with depinning criticality-driven spatial correlations.

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.