Interface Motion in Random Media at Finite Temperature

TL;DR

This study numerically investigates the dynamics of driven elastic interfaces in random media, revealing the significant role of thermal effects on depinning and avalanche behavior at finite temperatures.

Contribution

It provides detailed numerical analysis of thermal rounding of depinning and avalanche distributions, confirming theoretical predictions for elastic interfaces in disordered media.

Findings

Thermal effects are more significant than simple estimates suggest.

Creep velocity follows a power-law dependence on temperature at the depinning threshold.

Avalanche size distribution decays as a power law with exponent approximately -1.05.

Abstract

We have studied numerically the dynamics of a driven elastic interface in a random medium, focusing on the thermal rounding of the depinning transition and on the behavior in the $T=0$ pinned phase. Thermal effects are quantitatively more important than expected from simple dimensional estimates. For sufficient low temperature the creep velocity at a driving force equal to the $T=0$ depinning force exhibits a power-law dependence on $T$, in agreement with earlier theoretical and numerical predictions for CDW's. We have also examined the dynamics in the $T=0$ pinned phase resulting from slowly increasing the driving force towards threshold. The distribution of avalanche sizes $S_\|$ decays as $S_\|^{-1-\kappa}$, with $\kappa = 0.05\pm 0.05$, in agreement with recent theoretical predictions.