Temporal characteristics in nonequilibrium surface-growth models

We present analytical and numerical results showing 1/${\mathit{f}}^{\mathrm{\omega }}$ characteristics in the time series of growth velocity in a class of surface-growth models. The exponent ω is found to be related to the scaling exponents by ω=(2α-z+d-1)/z. The time series of surface width in the steady state are also shown to have power-law scalings in the frequency domain. We establish a mapping between the single-step model for ballistic growth and a random cellular automaton. We conclude that the steady state of the surface-growth models, in particular the ballistic deposition model, is a self-organized critical state.