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 α≥1 for these models. This implies anomalous behavior for the scaling of the height-difference correlation function G(x)=〈‖h(x)-h(0)${\mathrm{\Vert }}^2$〉 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.