Interfacial depinning transitions in disordered media: revisiting an old   puzzle
  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. 
Bel\'en Moglia, Ezequiel V. Albano, Pablo Villegas, Miguel A. Mu\~noz
cond-mat.stat-mech