  Using kinetic Monte Carlo simulations and a bond-counting ansatz, thermal
stability and diffusion of an adatom island on a crystal surface are studied.
At low temperatures, the diffusion constant $D$ is found to decrease for a wide
range of island sizes like $D \propto N^{-\alpha}$, where $\alpha$ is close to
one, $N$ being the number of adatoms in the cluster. By heating up the surface,
the system undergoes a phase transition above which the island disappears.
Characteristics of that transition are discussed.
