Elastic String in a Random Potential

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 $\zeta =0.24\pm 0.1$, or by a logarithm, $v_d\sim 1/\ln (F-F_T)$. The divergence of the velocity-velocity correlation length at threshold is characterized by an exponent $\nu =1.05\pm 0.1$.

12 pages + 3 Postscript figures

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