Association Problem in Statistical Mechanics—Critique of the Treatment of H. S. Green and R. Leipnik

It is pointed out that the Green- Leipnik solution of a two-dimensional lattice combinatorial problem (association problem) is manifestly incorrect. The reason for the error is shown to be a fallacious assumption made when applying the general mathematical theory to the problem which corresponds to distributing bonds over a plane p by q quadratic lattice (pq = n). The solutions quoted for various one-dimensional association problems are correct, but these problems can be solved more readily by an elementary direct argument. The present result can also be obtained from the Green-Leipnik approach if their assumption is corrected, but the labor involved is considerable and leads to a 17 x 17 matrix and most cross terms must be considered. The full two-dimensional case does not yield to either of these approaches and still represents a challenging problem. (B.O.G.)