Interface Depinning in a Disordered Medium - Numerical Results

TL;DR

This paper introduces a lattice model to numerically analyze the depinning transition of interfaces in disordered media, determining critical exponents and comparing results with theoretical predictions.

Contribution

It provides new numerical estimates of critical exponents for interface depinning in 1+1 and 2+1 dimensions, supporting the functional renormalization group approach.

Findings

Critical exponents are numerically determined for 1+1 and 2+1 dimensions.

Results align with recent analytical and numerical studies.

Supports the universality class predicted by the functional renormalization group.

Abstract

We propose a lattice model to study the dynamics of a driven interface in a medium with random pinning forces. For driving forces F smaller than a threshold force F_c the whole interface gets pinned. The depinning transition can be characterized by a set of critical exponents: the static and dynamical roughness exponent, the velocity exponent defined by the scaling of the velocity of the interface with F-F_c, and a correlation length exponent. The critical exponents are determined numerically in 1+1 and 2+1 dimensions. Our findings are compared with recent numerical and analytical results for a Langevin equation with quenched noise, which is expected to be in the same universality class. Our results support a recent functional renormalization group calculation by T.Nattermann et.al. (J.Phys.II France 2, 1483 (1992)).