Nucleation and growth in systems with many stable phases

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Abstract
We study the kinetics of nucleation and growth in systems with an arbitrary number of distinct stable phases for both homogeneous and heterogeneous nucleation. Exact solutions for the phase transformation kinetics in one dimension are obtained and compared with the mean-field results. We have observed anomalous power-law asymptotics for both homogeneous and heterogeneous nucleation in one dimension, while the mean-field theory predicts exponential asymptotic behavior for large times. Numerical simulations for 2d systems show that the mean-field theory is surprisingly accurate. Some properties of the spatial patterns at the final stage of nucleation and growth are elucidated.