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The Unusual Universality of Branching Interfaces in Random Media

Mehran Kardar·Attilio L. Stella·Giovanni Sartoni·Bernard Derrida
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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.

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Mehran Kardar, Attilio L. Stella, Giovanni Sartoni, Bernard Derrida. 1994-12-05. The Unusual Universality of Branching Interfaces in Random Media. https://doi.org/10.1103/physreve.52.r1269

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