Slow Crossover to Kardar-Parisi-Zhang Scaling

The Kardar-Parisi-Zhang (KPZ) equation is accepted as a generic description of interfacial growth. In several recent studies, however, values of the roughness exponent alpha have been reported that are significantly less than that associated with the KPZ equation. A feature common to these studies is the presence of holes (bubbles and overhangs) in the bulk and an interface that is smeared out. We study a model of this type in which the density of the bulk and sharpness of the interface can be adjusted by a single parameter. Through theoretical considerations and the study of a simplified model we determine that the presence of holes does not affect the asymptotic KPZ scaling. Moreover, based on our numerics, we propose a simple form for the crossover to the KPZ regime.