Transitions in a probabilistic interface growth model

Abstract

We study a generalization of the Wolf–Villain (WV) interface growth model based on aprobabilistic growth rule. In the WV model, particles are randomly deposited onto asubstrate and subsequently move to a position nearby where the binding is strongest. Weintroduce a growth probability which is proportional to a power of the numberni of bindingsof the site i: . Through extensive simulations, in(1 + 1) dimensions, we find three behaviors depending on theν value: (i) ifν is small, acrossover from the Mullins–Herring to the Edwards–Wilkinson (EW) universality class; (ii) for intermediatevalues of ν, a crossover from the EW to the Kardar–Parisi–Zhang (KPZ) universality class; and, finally, (iii) forlarge ν values, the system is always in the KPZ class. In(2 + 1) dimensions, we obtain three different behaviors: (i) a crossover fromthe Villain–Lai–Das Sarma to the EW universality class for smallν values; (ii) the EW class is always present for intermediateν values; and (iii) a deviation from the EW class is observed for largeν values.