Scaling Behavior of Driven Interfaces Above the Depinning Transition

TL;DR

This paper investigates the scaling behavior of driven interfaces near the depinning transition, revealing class-dependent roughness exponent changes and proposing scaling relations that connect exponents across the transition.

Contribution

It identifies distinct behaviors of the roughness exponent at the transition for different universality classes and introduces new scaling relations linking exponents on both sides.

Findings

Roughness exponent changes at the transition for one universality class.

Dynamical exponent remains unchanged across the transition.

Prefactor of the width scales with the driving force.

Abstract

We study the depinning transition for models representative of each of the two universality classes of interface roughening with quenched disorder. For one of the universality classes, the roughness exponent changes value at the transition, while the dynamical exponent remains unchanged. We also find that the prefactor of the width scales with the driving force. We propose several scaling relations connecting the values of the exponents on both sides of the transition, and discuss some experimental results in light of these findings.