A new approach to the CPA and its generalizations

A new technique for evaluating configurationally averaged properties of disordered systems due to Mookerjee (see abstr. A43969 of 1973) is examined. Attention is focused on the site-diagonal element of the single-particle Green function in the Anderson model of cellular disorder, and single-site coherent potential approximation (CPA) is shown to arise naturally within this new formalism. Generalizations to n site and cluster approximations then follow in a very direct and instructive fashion. Necessary analytic properties of the single-particle Green functions are an immediate corollary of the method. Numerical results are presented for the bimodally disordered tight-binding linear chain.