Abstract
We derive the phenomenological dynamics of interfaces from stochastic “microscopic” models. The main emphasis is on models with a nonconserved order parameter. A slowly varying interface has then a local normal velocity proportional to the local mean curvature. We study bulk models and effective interface models and obtain Green-Kubo-like expressions for the mobility. Also discussed are interface motion in the case of a conserved order parameter, pure surface diffusion, and interface fluctuations. For the two-dimensional Ising model at zero temperature, motion by mean curvature is established rigorously.
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Spohn, H. Interface motion in models with stochastic dynamics. J Stat Phys 71, 1081–1132 (1993). https://doi.org/10.1007/BF01049962
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DOI: https://doi.org/10.1007/BF01049962