The theory of disordered alloys II: continued fractions and cluster theory

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Abstract
A continued fraction method for calculating the density of states due to Haydock and others is applied to a commonly used model Hamiltonian for a disordered alloy. The density of states may be calculated with great ease from this method and suffers from none of the analytic difficulties which bedevil selfconsistent cluster theory methods based on the coherent potential approximation. The density of states has been calculated for a simple cubic crystal and displays in the minority band and sometimes in the majority band) peaks which are related to the levels of isolated clusters containing one, two, three or several minority (or majority) atoms. The method has the virtue also of enabling the Lifshitz condition on the density of states to be satisfied although this is done in a slightly artificial manner.

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