Dynamics of a height-conserved surface-growth model with spatially correlated noise

Abstract

We investigate the effects of long-range correlated noise on the dynamics of a growing interface in which the total volume under the interface is conserved. For a nonconserved noise the model corresponds to the nonlinear molecular-beam-epitaxy model with spatially correlated noise. We use both a dynamic renormalization-group approach and a Kolmogorov type of scaling applied to the Langevin equation describing the model, to study the dynamical evolution of the interface in arbitrary interface dimension d’. We find that for d’<2 any amount of spatial correlation is relevant and leads to a universality class different from that of the uncorrelated white noise. Both methods are found to give the same expressions for the growth exponents α and β as a function of the noise parameter and the spatial dimension of the system. These exponents are expected to be exact because of nonrenormalization of the spectral density function and the vertex function.