Universality in two- and three-dimensional growth and deposition models

We simulate the three-dimensional single-step model of deposition and evaporation as well as a three-dimensional ballistic-deposition model with surface diffusion. We find that the dynamic structure factor S(k,t) obeys dynamic scaling: S(k,t)∼$k^{\mathrm{-}2+\eta }$g($k^z$t), where in all three-dimensional cases studied z-η/2≊2, consistent with a recently proposed scaling law. For the single-step model z=2 if the process is time-reversal invariant, z≊1.63 if it is not. The ballistic-deposition model seems to have the dynamic exponent z=2 in both two and three dimensions. These results are discussed in the context of the Burgers equation which has been proposed as a model for interface dynamics.