Relaxation function and dynamic exponent for discrete growth models

We develop a new method of measuring the dynamic exponent z for discrete growth models. Starting from a sinusoidal initial surface of a selected wavelength l, we consider a relaxation function R(t,l), which is a quantity similar to the autocorrelation function of the surface height. Typically the relaxation function decays exponentially following e−g(t/τ(l)), where τ(l) is the relaxation time and it depends on the wavelength l. The dynamic exponent z is measured by the relation τ(l) lz. We find that g(x) scales as x1.0 for the Family model and as x1.5 for the restricted solid-on-solid model. The advantages of the method are also discussed.