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A simple model of epitaxial growth proposed by Wolf and Villain is investigated using extensive computer simulations. We find an unexpectedly complex crossover behavior of the original model in both 1+1 and 2+1 dimensions. A crossover from the effective growth exponent βeff{}0.37 to βeff{}0.33 is observed in 1+1 dimensions, whereas additional crossovers, which we believe are to the scaling behavior of an Edwards-Wilkinson type, are observed in both 1+1 and 2+1 dimensions. Anomalous scaling due to power-law growth of the average step height is found in 1+1 dimensions, and also at short time and length scales in 2+1 dimensions. The roughness exponents ζeffᶜ obtained from the height-height correlation functions in 1+1 dimensions ({}3/4) and 2+1 dimensions ({}2/3) cannot be simultaneously explained by any of the continuum equations proposed so far to describe epitaxial growth.
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Šmilauer et al. (1994) studied this question.
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