Interfacial depinning transitions in disordered media: revisiting an old puzzle

Abstract

Interfaces advancing through random media represent a number of different problems in physics, biology and other disciplines. Here, we study the pinning/depinning transition of the prototypical non-equilibrium interfacial model, i.e. the Kardar–Parisi–Zhang equation, advancing in a disordered medium. We will separately analyze the cases of positive and negative non-linearity coefficients, which are believed to exhibit qualitatively different behavior: the positive case shows a continuous transition that can be related to directed-percolation-depinning, while in the negative case there is a discontinuous transition and faceted interfaces appear. Some studies have argued from different perspectives that both cases share the same universal behavior. By using a number of computational and scaling techniques we will shed light on this puzzling situation and conclude that the two cases are intrinsically different.