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Stochastic Ising models and anisotropic front propagation. (English) Zbl 0937.82034
Summary: We study Ising models with general spin-flip dynamics obeying the detailed balance law. After passing to suitable macroscopic limits, we obtain interfaces moving with normal velocity depending anisotropically on their principal curvatures and direction. In addition we deduce (direction-dependent) Kubo-Green-type formulas for the mobility and the Hessian of the surface tension, thus obtaining an explicit description of anisotropy in terms of microscopic quantities. The choice of dynamics affects only the mobility, a scalar function of the direction.

MSC:
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
82C24 Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics
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