Anisotropic finite-size scaling of an elastic string at the depinning threshold in a random-periodic medium

Abstract

We numerically study the geometry of adrivene lasticstringatits sample-dependent depinningthres hold in random-periodic media. We find that the anisotropic finite-size scaling of the average square width ω 2 and of its associated probability distributionare both controlled by the ratio κ=M/L ζdep , where ζde is the random-manifold depinning roughness exponent L is the longitudinal size of the string and M the transverse periodicity of the random medium. The rescaled average square width ω 2 /L 2ζdep displays a non-trivial single minimum for a finite value of κ. We show that the initial decrease for small κ reflects the crossover at κ∼ 1 from the random-periodic to the random-manifold roughness. The increase for very large κ implies that the increasingly rare critical configurations, accompanying the crossover to Gumbel critical-force statistics, display anomalous roughness properties :atransverse-periodicity scaling in spitethat ω 2