Dynamics of surface roughening with quenched disorder.

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 ${d}_{\mathrm{min}}$ 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 ${d}_{\mathrm{min}}$ for percolation, from $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ to $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}6$.