Cs. Ryu et al., ANOMALOUS SCALING BEHAVIOR IN A SOLID-ON-SOLID MODEL FOR EPITAXIAL-GROWTH, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 54(1), 1996, pp. 284-288
We study the correlation function in a solid-on-solid model for epitax
ial growth on one-dimensional substrates. In the transient regime, we
find an anomalous situation that the roughness exponent (alpha approxi
mate to 1) obtained from the surface width is different from that (alp
ha' approximate to 0.75) of the correlation function, which is well de
scribed by the scaling hypotheses previously proposed by Schroeder et
al. [M. Schroeder, M. Siegert, D. E. Wolf, J. D. Shore, and M. Plischk
e, 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 correl
ation function in growth models with alpha less than or equal to 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 sca
le shows a power-law increase with time, the roughness exponent alpha'
measured in experiments should be converted to alpha determining the
universality classes.