Multiscale theory of fluctuating interfaces: renormalization of atomistic models

We describe a framework for the multiscale analysis of atomistic surface processes which we apply to a model of homoepitaxial growth with deposition according to the Wolf-Villain model and concurrent surface diffusion. Coarse graining is accomplished by calculating renormalization-group (RG) trajectories from initial conditions determined by the regularized atomistic theory. All of the crossover and asymptotic scaling regimes known from computer simulations are obtained, but we also find that two-dimensional substrates show an intriguing transition from smooth to mounded morphologies along the RG trajectory.