Dendritic growth in a mean-field lattice gas model

We study a stochastic lattice gas model with attractive nearest-neighbor interaction. In a mean-field approximation, its local master equation can be written as a generalized Cahn-Hilliard equation. Numerical simulations in two dimensions show the growth of regular snowflakes. Our microscopic equation of motion naturally shows curvature and kinetic effects at the interface as assumed by the classic phenomenological equations of dendritic growth. In addition, we find solute trapping. The dendrite tips are stabilized by the Gibbs-Thomson boundary condition. We calculate the surface tension and show that it has the expected angular variation. Some numerical results for the kinetic coefficient are given. We compare our model to other microscopic growth models and the phase-field models, and discuss the influence of noise.