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

• Main Authors: Sebastián Bustingorry, Alejandro B. Kolton
• Format: Article
• Language: English
• Published: Papers in Physics 2010-02-01
• Series: Papers in Physics
• Subjects: Depinning Transition; Disordered Elastic Systems
• Online Access: http://www.papersinphysics.org/index.php/papersinphysics/article/view/44/pdf44

<p>We&nbsp;numerically&nbsp;study the geometry of a driven elastic string at its sample-dependent depinning threshold in random-periodic media. We find that the anisotropic finite-size scaling of the average square width $overline{w^2}$ and of its associated probability distribution are both controlled by the ratio $k=M/L^{zeta_{dep}}$, where $zeta_{dep}$ 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 $overline{w^2}/L^{2zeta_{dep}}$ displays a non-trivial single minimum for a finite value of $k$. We show that the initial decrease for small $k$ reflects the crossover at $k sim 1$ from the random-periodic to the random-manifold roughness. The increase for very large $k$ implies that the increasingly rare critical configurations, accompanying the crossover to Gumbel critical-force statistics, display anomalous roughness properties: a transverse-periodicity scaling in spite that $overline{w^2} ll M$, and subleading corrections to the standard random-manifold longitudinal-size scaling. Our results are relevant tounderstanding the dimensional crossover from interface to particle depinning.</p><p>&nbsp;</p><p><strong>Received:</strong> 20 October 2010,&nbsp;<strong></strong><strong>Accepted:</strong> 1 December 2010; <strong>Edited by:</strong>&nbsp; A. Vindigni; <strong>Reviewed by:</strong> A. A. Fedorenko, CNRS-Lab. de Physique, ENS de Lyon, France; <strong>DOI:</strong> 10.4279/PIP.020008</p>