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

Abstract

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 ) ⟩ ⟨ w 2 ( 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 and follows the relation R(L, t) ∼ 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) ∼ t 1/z for the RSOS model in higher dimensions.