Dynamics of Surface Roughening with Quenched Disorder

TL;DR

This paper investigates the dynamical exponent in surface roughening models with quenched disorder, proposing a relation to shortest path exponents in percolation, supported by simulations across multiple dimensions.

Contribution

It establishes a novel theoretical link between the dynamical exponent in surface roughening and the shortest path exponent in isotropic percolation, validated through extensive simulations.

Findings

The dynamical exponent z equals the shortest path exponent d_min in the corresponding percolation cluster.

Simulation results confirm the proposed relation for dimensions 1 through 6.

The study enhances understanding of surface roughening dynamics in disordered systems.

Abstract

We study the dynamical exponent $z$ for the directed percolation depinning (DPD) class of models for surface roughening in the presence of quenched disorder. We argue that $z$ for $(d+1)$ dimensions is equal to the exponent $d_{\rm min}$ characterizing the shortest path between two sites in an isotropic percolation cluster in $d$ dimensions. To test the argument, we perform simulations and calculate $z$ for DPD, and $d_{\rm min}$ for percolation, from $d = 1$ to $d = 6$.