Interfacial depinning transitions in disordered media: revisiting an old puzzle

TL;DR

This paper investigates the pinning/depinning transition of interfaces in disordered media using the KPZ equation, revealing fundamental differences between positive and negative non-linearity cases through computational and scaling analyses.

Contribution

It provides a detailed analysis distinguishing the universal behaviors of positive and negative non-linearity cases in the KPZ model, challenging previous claims of their similarity.

Findings

Positive case exhibits a continuous transition related to directed percolation.

Negative case shows a discontinuous transition with faceted interfaces.

The two cases are intrinsically different in their universal behavior.

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 analyze separately 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. Here, by using a number of computational and scaling techniques we shed light on this puzzling situation and conclude that the two cases are intrinsically different.