Analyticity of Homomorphic Cluster Coherent Potential Approximation

We propose one possible way of avoiding the breakdown of analyticity ofaverage Green's functions based on the cluster coherent potential approximationfor substitutionally disordered systems. Our assertion is that nonanalyticitywould not occur when a one-particle total hamiltonian is partitioned into the sumof homomorphic single-cluster hamiltonians and the CPA condition is appliedto one of these homomorphic subhamiltonians. Using an example of homo-morphic partition into double-site clusters, we show that the results for disorderedone- and three-dimensional systems with site-diagonal randomness lend supportto our assertion.