Short-range versus long-range order in a model binary alloy

We calculate the free energy of a linear binary metallic alloy using an exact transfer-matrix formalism. We obtain for the first time the electronic band structure when there is nonvanishing short-range order and calculate the temperature dependence of the short-range order parameter. Following Foo and Amar, we also introduce long-range order via two sublattices, but we find this necessarily raises the free energy. We conclude that the first-order phase transition of Foo and Amar is spurious, being an artifact of their assumption of long-range order and neglect of short-range order.