We study the dynamics of an interface driven far from equilibrium in three dimensions. First we derive the Kardar-Parisi-Zhang equation from the Langevin equation for a system with a nonconserved scalar order parameter, for the cases where an external field is present, and where an asymmetric coupling to a conserved variable exists. The relationship of the phenomena to self-organized critical phenomena is discussed. Numerical results are then obtained for three models that simulate the growth of an interface: the Kardar-Parisi-Zhang equation, a discrete version of that model, and a solid-on-solid model with asymmetric rates of evaporation and condensation. We first make a study of crossover effects. In particular, we propose a crossover scaling ansatz and verify it numerically. We then estimate the dynamical scaling exponents. Within the precision of our study, the Kardar-Parisi-Zhang equation and the solid-on-solid model have the same asymptotic behavior, indicating that the models share a dynamical universality class. Furthermore, the discrete models exhibit a kinetic roughening transition. We study this by monitoring the surface step energy, which shows a dramatic jump at a finite temperature for a given driving force. At the same temperature, a finite-size-scaling analysis of the bond-energy fluctuation shows a diverging peak.

• Received 3 August 1990

DOI:https://doi.org/10.1103/PhysRevA.43.1727