Relaxation function and dynamic exponent for discrete growth models

Abstract

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)∼ l z . We find that g( x) scales as x 1.0 for the Family model and as x 1.5 for the restricted solid-on-solid model. The advantages of the method are also discussed.