Diagram enumeration in the theory of magnetically dilute Heisenberg ferromagnets

This paper presents a direct mathematical proof of the correctness of the diagram counting procedures used by Morgan and Rushbrooke in their investigation of randomly dilute Heisenberg ferromagnets. The principal techniques used in accomplishing the proof are: (a) algebraic expression of the enumeration of diagram occurrences in terms of lattice sums over occupation variables and nearest-neighbour selector factors, and (b) the computation of the average values of these sums, averaged over all random configurations of the lattice. It is suggested that these techniques may be generally applicable to many other problems concerned with the lattice statistics of randomly mixed crystals.