Anisotropic surface growth model in disordered media

Abstract

We introduce a self-organized surface growth model in 2 + 1 dimensions with an anisotropic avalanche process, which is expected to be in the universality class of the anisotropic quenched Kardar-Parisi-Zhang (KPZ) equation with alternative signs of the nonlinear KPZ terms. It turns out that the surface height correlation function in each direction scales distinctively. The anisotropic behavior is attributed to the asymmetric behavior of the quenched KPZ equation in 1 + 1 dimensions with respect to the sign of the nonlinear KPZ term.