General Formulation of then-Site Coherent-Potential Approximation for a Disordered Medium

The $n$-site coherent-potential approximation of Nickel and Krumhansl is given a general formulation suited to a wide class of problems involving correlated disordered media. The application of the method to the calculations of static and dynamical properties of substitutional alloys, fluids, and elastic solids is presented, providing systematic generalizations of the treatments of Taylor, Faulkner, and Velický. The problem of analyticity of the mean resolvent, raised by Nickel Butler in the case of substitutional alloys, is discussed briefly, but not resolved.