Ostwald ripening of faceted two-dimensional islands

We study Ostwald ripening of two-dimensional adatom and advacancy islands on a crystal surface by means of kinetic Monte Carlo simulations. At large bond energies, the islands are square shaped, which qualitatively changes the coarsening kinetics. The Gibbs-Thomson chemical potential is violated: the coarsening proceeds through a sequence of ``magic'' sizes corresponding to square or rectangular islands. The coarsening becomes attachment limited, the asymptotic law is reached only after a very long transient time. The unusual coarsening kinetics obtained in the Monte Carlo simulations is well described by the Becker-D\"oring equations of nucleation kinetics. These equations can be applied to a wide range of coarsening problems.