Elastic String in a Random Potential

TL;DR

This study numerically investigates the depinning transition of a driven elastic string in a 2D random medium, revealing critical scaling behavior and divergence of correlation length at the threshold force.

Contribution

It provides the first detailed numerical analysis of the critical dynamics and scaling laws of an elastic string in a quenched random potential.

Findings

Identified a critical force $F_T$ for depinning.

Found velocity scales as a power law or logarithm near threshold.

Measured divergence of correlation length with exponent $ u=1.05\

Abstract

We have studied numerically the dynamics of a directed elastic string in a two-dimensional array of quenched random impurities. The string is driven by a constant transverse force and thermal fluctuations are neglected. There is a transition from pinned to unpinned behavior at a critical value $F_T$ of the driving force. At the transition the average string velocity scales with the driving force. The scaling is equally well described by a power law $v_d\sim (F-F_T)^\zeta$, with $\zeta=0.24\pm0.1$, or by a logarithm, $v_d\sim1/\ln(F-F_T)$. The divergence of the velocity-velocity correlation length at threshold is characterized by an exponent $\nu=1.05\pm0.1$.