Universality of critically pinned interfaces in 2-dimensional isotropic random media

TL;DR

This paper conjectures that in 2D isotropic random media, critically pinned interfaces universally belong to the ordinary percolation class, regardless of specific model details, contrasting higher-dimensional cases.

Contribution

It proposes a universality conjecture for critically pinned interfaces in 2D isotropic media, supported by extensive simulations, unifying various models under the percolation universality class.

Findings

Interfaces in 2D isotropic media follow ordinary percolation universality.

No distinction between fractal and rough interfaces in 2D isotropic media.

Universality applies to multiple models like RFIM, bootstrap percolation, and SWIR epidemics.

Abstract

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