Nonuniversality in models of epitaxial growth

Kinetic roughening in two variants of a solid-on-solid model of epitaxial growth, a ``toy'' relaxation model and a collective diffusion model, is studied and compared, using extensive computer simulations in different spatial dimensions. We have studied the Wolf-Villain (WV) model and its modifications, and a full diffusion (FD) model with Arrhenius dynamics. The WV model shows nonuniversal features and its asymptotic behavior switches between the Edwards-Wilkinson type and a morphological instability, depending on the spatial dimension, a lattice coordination, or a minor modification of the model rules. The results for the FD model in 1+1 and 2+1 dimensions are not consistent with any of the continuum equations proposed to describe epitaxial growth; in particular, we observe too low values of the roughness exponent measured from the height-difference correlation function. In 1+1 dimensions, the results obtained for both models are very similar for more than 10⁶ monolayers deposited with an ``incorporation'' radius in the WV model corresponding to the substrate temperature in the FD model. Such a close correspondence is not found in 2+1 dimensions. Asymptotic behavior of the WV and FD models is different in all spatial dimensions. Both FD and WV models show anomalous scaling in all dimensions studied. The anomalous scaling in the FD model is very weak (logarithmic) in the physically relevant case of 2+1 dimensions. {} 1996 The American Physical Society.