Stochastic Ising models and anisotropic front propagation.

*(English)*Zbl 0937.82034Summary: 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 |

##### Keywords:

Ising model with general spin flip dynamics; interfaces; anisotropy; motion curvature; Kubo-Green formulas for mobility and surface tension
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\textit{M. A. Katsoulakis} and \textit{P. E. Souganidis}, J. Stat. Phys. 87, No. 1--2, 63--89 (1997; Zbl 0937.82034)

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