Occam’s razor on surfaces: renormalization of microscopic processes

Abstract

We describe a methodology for the expression of atomistic models of fluctuating interfacesas continuum equations. We begin with formally exact Langevin equations based on theatomistic transition rules, which are regularized to produce stochastic partial differentialequations. Subsequent coarse graining is accomplished by calculating renormalization-group(RG) trajectories from initial conditions determined by the regularized equations. The RGanalysis shows that the morphological manifestation of a given atomistic relaxationmechanism can depend on the length scales and timescales considered as well as on thedimensionality of the fluctuating interface. Even complex surface processes, after amoderate degree of coarse graining, are reduced to low-order stochastic partialdifferential equations. We illustrate these ideas with a model of a growing surfaceunder the competition between the deposition of new material and the subsequentrelaxation through surface diffusion. We conclude with an augmentation of ourdifferential equations with a pinning term to account for lattice effects in theearly stages of growth, where surface electron diffraction oscillations indicatelayer-by-layer growth. The calculation of submonolayer morphology, which is composed ofseparated monolayer islands, provides an illustration of the efficacy of our method.