  The nucleation and growth of two--dimensional islands is studied with Monte
Carlo simulations of a pair--bond solid--on--solid model of epitaxial growth.
The conventional description of this problem in terms of a well--defined
critical island size fails because no islands are absolutely stable against
single atom detachment by thermal bond breaking. When two--bond scission is
negligible, we find that the ratio of the dimer dissociation rate to the rate
of adatom capture by dimers uniquely indexes both the island size distribution
scaling function and the dependence of the island density on the flux and the
substrate temperature. Effective pair-bond model parameters are found that
yield excellent quantitative agreement with scaling functions measured for
Fe/Fe(001).

Condensed Matter