Roughening Transition of Interfaces in Disordered Systems

TL;DR

This paper investigates the disorder-driven roughening transition of interfaces in disordered systems, revealing a continuous transition with superuniversal properties for dimensions between 2 and 4, using scaling and renormalization methods.

Contribution

It demonstrates for the first time a continuous disorder-driven roughening transition in interfaces for 2<D<4, with calculated critical exponents and superuniversal roughness at the transition.

Findings

Continuous roughening transition for 2<D<4

Superuniversal logarithmic roughness at criticality

No transition at the upper critical dimension D_c=4

Abstract

The behavior of interfaces in the presence of both lattice pinning and random field (RF) or random bond (RB) disorder is studied using scaling arguments and functional renormalization techniques. For the first time we show that there is a continuous disorder driven roughening transition from a flat to a rough state for internal interface dimensions 2<D<4. The critical exponents are calculated in an \epsilon-expansion. At the transition the interface shows a superuniversal logarithmic roughness for both RF and RB systems. A transition does not exist at the upper critical dimension D_c=4. The transition is expected to be observable in systems with dipolar interactions by tuning the temperature.