UNUSUAL UNIVERSALITY OF BRANCHING INTERFACES IN RANDOM-MEDIA

We study the criticality of a Potts interface by introducing a froth model which, unlike its solid-on-solid 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 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.