Unusual universality of branching interfaces in random media.

We study the criticality of a Potts interface by introducing a 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 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. Pacs numbers: 05.70.Jk, 68.35.Rh, 75.10.Hk, 82.65.Dp Typeset using REVTEX