Exact Occupation Statistics for One-Dimensional Arrays of Dumbbells

Abstract

Exact relationships are developed which describe the occupation statistics for one-dimensional arrays of dumbbells. It is shown that in the limit, as the number of compartments per array tends to infinity, these relationships reduce to those calculated, using the Bethe approximation when the number of nearest neighbors is two. A partition function, which includes the influence of the configurational correlation inherent in a one-dimensional array of dumbbells, is also derived and discussed.