GROOVE INSTABILITIES IN SURFACE GROWTH WITH DIFFUSION

The existence of a grooved phase in linear and nonlinear models of sur face growth with horizontal diffusion is studied in d = 2 and 3 dimens ions. We show that the presence of a macroscopic groove, i.e., an inst ability towards the creation of large slopes and the existence of a di verging persistence length in the steady state, does not require highe r-order nonlinearities but is a consequence of the fact that the rough ness exponent alpha greater-than-or-equal-to 1 for these models. This implies anomalous behavior for the scaling of the height-difference co rrelation function G(x) = [\h(x)-h(0)\2] which is explicitly calculate d for the linear diffusion equation with noise in d = 2 and 3 dimensio ns. The results of numerical simulations of continuum equations and di screte models are also presented and compared with relevant models.