THEORETICAL DETERMINATION OF N-SITE CONFIGURATION PROBABILITIES FROM PAIR CORRELATIONS IN BINARY LATTICES

A new variational method is presented for determining configuration probabilities of three or more sites in partially ordered binary lattices from pair correlation data. The method is tested for several cases where the exact solution is known by independent means, and it is shown to yield the correct result in each case. It is suggested but not proven that the method is exact for all applications where the configurational energy of the lattice remains constant during the variational procedure. Comparison is made with the Superposition Approximation of Kirkwood and with Monte Carlo studies. In addition, the method is shown to bear an inverse relationship to the Cluster Variation Method. It is concluded that this new variational procedure should be quite useful for obtaining a more complete microscopic description of a partially ordered lattice than is presently available with the pair configurations picture. © 1969.