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

Abstract

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 nucleus is almost a perfect square. Spins are randomly flipped via Metropolis-type dynamics. At moderately strong undercoolings, the step nucleation rates can be evaluated from the first principles. This permits the description of the growth of an infinite interface using a step-on-step nucleation picture. The averaged shape of the interface is universal (i.e., it does not depend on any parameters as long as the interface remains stable), and its growth rate, in appropriate variables, also has no free parameters. For finite sizes of two-dimensional crystals their growth can be dominated by nucleation of single steps, and becomes size-dependent. For both infinite- and finite-size interfaces growth rates are in good agreement with large-scale Monte Carlo simulations. At high undercoolings the interface becomes very rough, in which case the crystals switch to circular shapes, in contrast to the equilibrium Wulff expectation.