DYNAMICAL UNIVERSALITY OF THE NONLINEAR CONSERVED CURRENT EQUATION FOR GROWING INTERFACES

A nonlinear growth equation recently proposed as a model for molecular beam epitaxy, h/t= -ν44h+λ222(h)2+λ13(h)3+η, where ν4,λ22, and λ12 are growth parameters and η is the deposition white noise, has been studied by a direct integration method. The standard deviation of the surface height for nonzero λ13 increases as t1/4 in 1+1 dimensions, where t is time, which is consistent with the universality class of the Edwards- and Wilkinson-type [Proc. R. Soc. London Ser. A 381, 17 (1982)] growth equation h/t=ν22h+η, where nu sub 2- is the Edwards-Wilkinson growth parameter. This disagrees with the previous results obtained by dimensional scaling analysis. For λ13=0, our results are in agreement with known analytic results. Possible implications of our results for conserved growth are discussed. © 1995 The American Physical Society.