Exact results for a three-dimensional alloy with site diagonal disorder: comparison with the coherent potential approximation

Densities of states and spectral functions are obtained for large ({~}8000 atoms) three-dimensional alloy models with cell localized disorder and are compared with the single-site coherent-potential approximation (CPA). We find that the CPA agrees remarkably well with the exact numerical results. In particular, the overall structure of the electronic spectrum and the transition from one- to two-band behavior are well described. There is, however, some substructure which is not reproduced by the single-site approximation.