Ordering in random overlayers: the correlated cluster mean-field method.

We have extended a recently proposed correlated cluster mean-field (CCMF) theory to two-dimensional binary alloys with interactions up to the next-nearest neighbors and investigated their critical behavior. A very good agreement with results from the renormalization group theory was obtained for the critical temperatures of a simple model. We finally successfully compared our results obtained using the CCMF with the results of Monte Carlo simulations for the case of ordering in a random Fe(0.5)Co(0.5) overlayer on the Cu(001) substrate. The proposed theory represents a numerically efficient alternative to existing approaches like the cluster variation method and Monte Carlo simulations.