Anomalous roughening in growth processes

Abstract

We study the roughening of a growing surface near to a morphological transition within a general scaling framework. For a class of systems, where the transition can be related to directed percolation, the anomalous roughness at the critical point is at most logarithmical. In two-dimensional simulations we find ${\mathrm{w}}^{2}$\ensuremath{\sim}logL where w is the width of the surface and L is the substrate size.