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Occam's razor on surfaces: Renormalization of microscopic processes

Abstract:

We describe a methodology for the expression of atomistic models of fluctuating interfaces as continuum equations. We begin with formally exact Langevin equations based on the atomistic transition rules, which are regularized to produce stochastic partial differential equations. Subsequent coarse graining is accomplished by calculating renormalization-group (RG) trajectories from initial conditions determined by the regularized equations. The RG analysis shows that the morphological manifestation of a given atomistic relaxation mechanism can depend on the length scales and timescales considered as well as on the dimensionality of the fluctuating interface. Even complex surface processes, after a moderate degree of coarse graining, are reduced to low-order stochastic partial differential equations. We illustrate these ideas with a model of a growing surface under the competition between the deposition of new material and the subsequent relaxation through surface diffusion. We conclude with an augmentation of our differential equations with a pinning term to account for lattice effects in the early stages of growth, where surface electron diffraction oscillations indicate layer-by-layer growth. The calculation of submonolayer morphology, which is composed of separated monolayer islands, provides an illustration of the efficacy of our method. © IOP Publishing Ltd.