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A simple model of epitaxial growth proposed by Wolf and Villain isinvestigated using extensive computer simulations. We find an unexpectedlycomplex crossover behavior of the original model in both 1+1 and 2+1dimensions. A crossover from the effective growth exponent $\beta_{\rmeff}\!\approx\!0.37$ to $\beta_{\rm eff}\!\approx\!0.33$ is observed in 1+1dimensions, whereas additional crossovers, which we believe are to the scalingbehavior of an Edwards--Wilkinson type, are observed in both 1+1 and 2+1dimensions. Anomalous scaling due to power--law growth of the average stepheight is found in 1+1 D, and also at short time and length scales in 2+1~D.The roughness exponents $\zeta_{\rm eff}^{\rm c}$ obtained from theheight--height correlation functions in 1+1~D ($\approx\!3/4$) and 2+1~D($\approx\!2/3$) cannot be simultaneously explained by any of the continuumequations proposed so far to describe epitaxial growth.Comment: 11 pages, REVTeX 3.0, IC-DDV-93-00

Crossover effects in the Wolf-Villain model of epitaxial growth in 1+1 and 2+1 dimensions