The Unusual Universality of Branching Interfaces in Random Media

TL;DR

This paper investigates the critical behavior of Potts interfaces in random media, revealing a universal linear interface at transition points and proposing a link between random Potts and Ising models.

Contribution

It introduces a froth model with bubbles of different phases and suggests a mechanism for the equivalence of critical random Potts and Ising models.

Findings

Interface becomes linear at criticality due to disorder effects

Probability of loop formation vanishes at transition

Proposes a universal behavior of interfaces in random media

Abstract

We study the criticality of a Potts interface by introducing a {\it froth} model which, unlike its SOS Ising counterpart, incorporates bubbles of different phases. The interface is fractal at the phase transition of a pure system. However, a position space approximation suggests that the probability of loop formation vanishes marginally at a transition dominated by {\it strong random bond disorder}. This implies a linear critical interface, and provides a mechanism for the conjectured equivalence of critical random Potts and Ising models.