We study the correlation function in a solid-on-solid model for epitaxial growth on one-dimensional substrates. In the transient regime, we find an anomalous situation that the roughness exponent (α≊1) obtained from the surface width is different from that (${\mathrm{\alpha }}^{\prime }$≊0.75) of the correlation function, which is well described by the scaling hypotheses previously proposed by Schroeder et al. [M. Schroeder, M. Siegert, D. E. Wolf, J. D. Shore, and M. Plischke, Europhys. Lett. 24, 563 (1993)] and Das Sarma, Ghaisas, and Kim [S. Das Sarma, S. V. Ghaisas, and J. M. Kim, Phys. Rev. E 49, 122 (1994)]. Few have been reported for anomalous scaling behaviors of the correlation function in growth models with α≤1. We also measure the surface width for various ranges in a fixed size of system as in experiments. In case a surface width for a very small scale shows a power-law increase with time, the roughness exponent ${\mathrm{\alpha }}^{\prime }$ measured in experiments should be converted to α determining the universality classes. © 1996 The American Physical Society.

• Received 4 December 1995

DOI:https://doi.org/10.1103/PhysRevE.54.284