Early-time regime for interfacial instabilities in a kinetic Ising model.

We have applied a Monte Carlo method to study the interfacial dynamics of a two-phase Ising lattice-gas system in two dimensions. Planar and circular interfaces are driven into nonequilibrium by a temperature gradient, and unstable modes develop causing one phase to grow into the other. We study the instability of the interface by monitoring the growth of these modes. In the case of a planar interface, a long-range interaction between the sites results in an extended linear regime where the modes grow exponentially in time, whereas, in the circular case, they grow only after the solid disk has exceeded a critical radius. We compare the data with linear stability analysis and find good agreement.