Uniqueness of the thermodynamic limit for driven disordered elastic interfaces

A. B. KOLTON; S. BUSTINGORRY; EDUARDO EZEQUIEL FERRERO; ALBERTO ROSSO

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

IOP PUBLISHING LTD

Lugar: Londres; Año: 2013 p. 12004 - 12014

1742-5468

We study the finite size fluctuations at the depinning transition for a one-dimensional elastic interface of size L displacing in a disordered medium of transverse size M=kLζ with periodic boundary conditions, where ζ is the depinning roughness exponent and k is a finite aspect ratio parameter. We focus on the crossover from the infinitely narrow (k→0) to the infinitely wide (k→∞) medium. We find that at the thermodynamic limit both the value of the critical force and the precise behavior of the velocity-force characteristics are {it unique} and k-independent. We also show that the finite size fluctuations of the critical force (bias and variance) as well as the global width of the interface cross over from a power-law to a logarithm as a function of k. Our results are relevant for understanding anisotropic size-effects in force-driven and velocity-driven interfaces.