Second-order phase transition in a model random alloy

We investigate the existence and stability of long-range order in a simple model of a binary alloy. We find that for electron concentrations in the vicinity of one per atom, in bipartite lattices, long-range order of the atoms exists at low temperatures, and we find that the system undergoes a second-order phase transition. We use a generalized form of the coherent-potential approximation (CPA) of Soven and find that this CPA reproduces exactly at least eight moments of the density of states. We derive an exact expression for the critical temperature when the alternating potential is much larger than the bandwidth.