GROOVE INSTABILITIES IN SURFACE GROWTH WITH DIFFUSION

The existence of a grooved phase in linear and nonlinear models of surface growth with horizontal diffusion is studied in d = 2 and 3 dimensions. We show that the presence of a macroscopic groove, i.e., an instability towards the creation of large slopes and the existence of a diverging persistence length in the steady state, does not require higher-order nonlinearities but is a consequence of the fact that the roughness exponent alpha greater-than-or-equal-to 1 for these models. This implies anomalous behavior for the scaling of the height-difference correlation function G(x) = [\h(x)-h(0)\2] which is explicitly calculated for the linear diffusion equation with noise in d = 2 and 3 dimensions. The results of numerical simulations of continuum equations and discrete models are also presented and compared with relevant models.