Analytic Properties of the Homomorphic Cluster Coherent Potential Approximation

Abstract

We show that the breakdown of analyticity is not found in average Green’s functions which are obtained on the basis of the cluster coherent potential approximation for systems with substitutional disorder if the one particle total hamiltonian for a given configuration is expressed as a sum of homomorphic single-cluster hamiltonians. Disorder can be site-diagonal and/or off-diagonal. In this article the emphasis is laid on off-diagonal cases. We first treat three-dimensional disordered systems with a semielliptic distribution of nearest neighbour transfers {V_ij}. We also apply our homomorphic cluster coherent approximation (HCPA) to the bond percolation problem; we obtain the densities of states which show characteristic features found through a computer simulation.