Driven Depinning in Anisotropic Media

TL;DR

This paper investigates how anisotropy in media affects the critical depinning behavior of driven interfaces, revealing different universality classes and anisotropic exponents, with exact results and scaling relations.

Contribution

It introduces a new understanding of depinning in anisotropic media, including exact exponents for tilted interfaces and scaling relations for pinned interfaces.

Findings

Depinning behavior depends on medium isotropy.

Different universality classes for hard and generic directions.

Exact exponents obtained via mapping to surface growth models.

Abstract

We show that the critical behavior of a driven interface, depinned from quenched random impurities, depends on the isotropy of the medium. In anisotropic media the interface is pinned by a bounding (conducting) surface characteristic of a model of mixed diodes and resistors. Different universality classes describe depinning along a hard and a generic direction. The exponents in the latter (tilted) case are highly anisotropic, and obtained exactly by a mapping to growing surfaces. Various scaling relations are proposed in the former case which explain a number of recent numerical observations.