Non-equilibrium interface of a two-dimensional low-temperature crystal

We study the interface in an Ising system with nearest-neighbor interaction on a square lattice at very low temperatures, when the Wulff shape of a nu cleus is almost a perfect square. Spins are randomly flipped via Metropolis -type dynamics. At moderately strong undercoolings, the step nucleation rat es can be evaluated from the first principles. This permits the description of the growth of an infinite interface using a step-on-step nucleation pic ture. The averaged shape of the interface is universal (i.e., it does not d epend on any parameters as long as the interface remains stable), and its g rowth rate, in appropriate variables, also has no free parameters. For fini te sizes of two-dimensional crystals their growth can be dominated by nucle ation of single steps. and becomes size-dependent. For both infinite- and f inite-size interfaces growth rates are in good agreement with large-scale M onte Carlo simulations. At high undercoolings the interface becomes very ro ugh, in which case the crystals switch to circular shapes, in contrast to t he equilibrium Wulff expectation. (C) 2000 Elsevier Science B.V. All rights reserved.