Exact nearest neighbor degeneracy for dumbbells on a one-dimensional lattice space

Abstract

Relationships are developed which describe exactly the degeneracy associated with nearest neighbor pairs of occupied sites (1–1), mixed sites (0–1), and vacant sites (0–0) for dumbbells distributed on a one‐dimensional lattice space. The first moments of these statistics are calculated, thereby permitting an evaluation of the error inherent in the use of the Bragg‐Williams approximation for this situation.