Dynamic finite-size scaling of the normalized height distribution in kinetic surface roughening.

Abstract

Using well-known simple growth models, we have studied the dynamic finite-size scaling theory for the normalized height distribution of a growing surface. We find a simple functional form that explains size-dependent behavior of the skewness and kurtosis in the transient regime, and obtain the transient- and long-time values of the skewness and kurtosis for the models. Scaled distributions of the models are obtained, and the shape of each distribution is discussed in terms of the interfacial width, skewness, and kurtosis, and compared with those for other models. Exponents eta(+) and eta(-), which characterize the form of the distribution, are determined from an exponential fitting of scaling functions. Our detailed results reveal that eta(+)+eta(-) approximately 4 for a model obeying usual scaling in contrast to eta(+)+eta(-)<4 with eta(-)=1 for a model exhibiting anomalous scaling as well as multiscaling. Since we obtain eta(+)+eta(-) approximately 4 for a model exhibiting anomalous scaling but no multiscaling, we conclude that the deviation from eta(+)+eta(-) approximately 4 is due to the presence of multiscaling behavior in a model.