The occupation statistics for indistinguishable dumbbells on a 2×2×N lattice space

Abstract

A 20-term recursion relation is derived that describes exactly the occupation statistics for indistinguishable dumbbells (which occupy two nearest neighbor sites) distributed on a 2×2×N lattice space. On the basis of this recursion, the normalization, expectation, dispersion, and continuous representation of the statistics are also developed. When the lattice space is completely filled, the recursion relationship reduces to four terms, permitting a calculation of the orientational degeneracy of a completely filled 2×2×N lattice space.