Surface pattern formation and scaling described by conserved lattice gases

We extend our 2 + 1 dimensional discrete growth model (PRE 79, 021125 (2009)) with a local exchange dynamics of octahedra, which describes surface diffusion. An inverse Mullins-Herring type of roughening process was realized by uphill diffusion of octahedra. By mapping the slopes on particles a two-dimensional, driven, nonequilibrium Ising model emerges in which the (smoothing/ roughening) surface diffusion can be described by the correlated (attracting/repelling) motion of dimers. We show that the pathological problem of freezing due to the short range jumps in a model, where the local height differences are restricted to ±1 can be overcome with the addition of a small external noise. In the limit of vanishing noise we provide numerical evidence for the Mullins-Herring class scaling by surface width scaling and roughness distribution studies. The competition of the inverse Mullins-Herring diffusion with a smoothing deposition which realizes a Kardar-Parisi-Zhang process one can generate different patterns: dots or ripples. We analyze numerically the scaling behavior and wavelength coarsening behavior in these models. In particular we confirm that the Kardar-Parisi-Zhang type of scaling is stable against surface diffusion, hence this is the asymptotic behavior of the Kuramoto-Sivashinsky equation as conjectured by field theory. In case of very strong, normal surface diffusion is added to KPZ we observe smooth surfaces with logarithmic growth, which can describe the mean-field KPZ behavior.