Elastic string in a random potential

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 ${\mathit{F}}_{\mathit{T}}$ 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 ${\mathit{v}}_{\mathit{d}}$∼(F-${\mathit{F}}_{\mathit{T}}$ ${)}^{\mathrm{\zeta }}$, with ζ=0.24±0.1, or by a logarithm, ${\mathit{v}}_{\mathit{d}}$∼1/ln(F-${\mathit{F}}_{\mathit{T}}$). The divergence of the velocity-velocity correlation length at threshold is characterized by an exponent ν=1.05±0.1.