Relaxation of particles in the sloped region in a conserved growth model

The dynamical scaling properties of conserved growth models, in which the downward (upward) movement of a particle dropped only on the sloped region occurs with a probability p (1-p), are investigated by simulations in the substrate dimension d=1. By direct analysis of the surface fluctuation W, the models with p>1/2 are clearly and cleanly shown to have crossover behavior from Mullins-Herring (MH) universality to Edwards-Wilkinson (EW) universality. In contrast, the models with p<1/2 are shown to have an instability eventually, even though they initially follow the MH equation. The model with p=1/2 is shown to belong to the MH universality class and to be the critical model that splits the models with EW behavior from those with the instability. From these results we explain the physical reason for the very slow crossover in models like the Wolf-Villain model.