Does the Quenched Kardar-Parisi-Zhang Equation Describe the Directed Percolation Depinning Models?

TL;DR

This study compares the quenched KPZ equation with directed percolation depinning models, revealing differences in growth mechanisms despite similar critical exponents, questioning the equation's adequacy in describing these models.

Contribution

It provides a detailed comparison of the QKPZ equation and DPD models, highlighting their differing growth contributions and challenging the assumption of their universality class equivalence.

Findings

Lateral contributions increase roughness near criticality in DPD models.

QKPZ equation's lateral contribution flattens roughness, unlike DPD models.

Similar critical exponents do not imply identical underlying mechanisms.

Abstract

The roughening of interfaces moving in inhomogeneous media is investigated by numerical integration of the phenomenological stochastic differential equation proposed by Kardar, Parisi, and Zhang [Phys. Rev. Lett. 56, 889, (1986)] with quenched noise (QKPZ). We express the evolution equations for the mean height and the roughness into two contributions: the local and the lateral one. We compare this two contributions with the ones obtained for two directed percolation deppining models (DPD): the Tang and Leschhorn model [Phys. Rev A 45, R8309 (1992)] and the Buldyrev et al. model [Phys. Rev. A 45, R8313 (1992)] by Braunstein al. [J. Phys. A 32, 1801 (1999); Phys. Rev. E 59, 4243 (1999)]. Even these models have being classified in the same universality class that the QKPZ the contributions to the growing mechanisms are quite different. The lateral contribution in the DPD models, leads to an increasing of the roughness near the criticality while in the QKPZ equation this contribution always flattens the roughness. These results suggest that the QKPZ equation does not describe properly the DPD models even when the exponents derived from this equation are similar to the one obtained from simulations of these models.