Thermal rounding exponent of the depinning transition of an elastic string in a random medium

TL;DR

This paper numerically investigates the thermal rounding exponent at the depinning transition of an elastic string in a disordered medium, finding a robust value of 0.15 that explains various scaling behaviors.

Contribution

The study provides the first numerical estimate of the thermal rounding exponent for elastic strings at depinning, confirming its consistency across multiple observables.

Findings

Thermal rounding exponent C6 = 0.15C2 is robust.

The exponent explains steady-state and transient scaling properties.

The results unify different observable behaviors under a common scaling framework.

Abstract

We study numerically thermal effects at the depinning transition of an elastic string driven in a two-dimensional uncorrelated disorder potential. The velocity of the string exactly at the sample critical force is shown to behave as $V \sim T^\psi$, with $\psi$ the thermal rounding exponent. We show that the computed value of the thermal rounding exponent, $\psi = 0.15$, is robust and accounts for the different scaling properties of several observables both in the steady-state and in the transient relaxation to the steady-state. In particular, we show the compatibility of the thermal rounding exponent with the scaling properties of the steady-state structure factor, the universal short-time dynamics of the transient velocity at the sample critical force, and the velocity scaling function describing the joint dependence of the steady-state velocity on the external drive and temperature.