A new way of measuring the correlation length in surface growth models

Abstract

We propose a new way of measuring the correlation length in surface growth processes. We define a quantity R(L,t) - (< w(4)(L,t)>/< w2(L,t)>(2) -1) L in d = 1 + 1, where w(t) and L are the surface width of a given sample at time t and the system size, respectively, and <...> denotes the average over samples. The quantity R(L, t) is proportional to the correlation length arid follows the relation R(L, t) similar to t(1/z) before the saturation for various growth models, where z is the dynamic exponent. The applicability of the method was examined for the restricted solid-on-solid (RSOS) model, equilibrium solid-on-solid model, and restricted curvature model. We also estimated z by using the relation R(t) similar to t(1/z) for the RSOS model in higher dimensions.