TY - JOUR
AU - Bustingorry, Sebastián
AU - Kolton, Alejandro B.
PY - 2010/12/20
Y2 - 2024/07/23
TI - Anisotropic finite-size scaling of an elastic string at the depinning threshold in a random-periodic medium
JF - Papers in Physics
JA - Pap. Phys.
VL - 2
IS - 0
SE - Articles
DO - 10.4279/pip.020008
UR - https://www.papersinphysics.org/papersinphysics/article/view/44
SP - 020008
AB - <p>We numerically 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 $\overline{w^2}/L^{2\zeta_{dep}}$ 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 to understanding the dimensional crossover from interface to particle depinning.</p><p> </p><p><strong>Received:</strong> 20 October 2010, <strong></strong><strong>Accepted:</strong> 1 December 2010; <strong>Edited by:</strong> 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>
ER -