Universality of Critically Pinned Interfaces in Two-Dimensional Isotropic Random Media

Based on extensive simulations, we conjecture that critically pinned interfaces in two-dimensionalisotropic random media with short-range correlations are always in the universality class of ordinarypercolation. Thus, in contrast to interfaces in > 2 dimensions, there is no distinction between fractal (i.e.,percolative) and rough but nonfractal interfaces. Our claim includes interfaces in zero-temperature randomfield Ising models (both with and without spontaneous nucleation), in heterogeneous bootstrap percolation,and in susceptible-weakened-infected-removed epidemics. It does not include models with long-rangecorrelations in the randomness and models where overhangs are explicitly forbidden (which would implynonisotropy of the medium)