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

We propose a new way of measuring the correlation length in surface growth processes. We define a quantity $R(L,t)=(\frac{⟨w^4(L,t)⟩}{{⟨w^2(L,t)⟩}^2}-1)L$ 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. (paper)