CVM Entropy Algebra

A concept of correlation correction factor (CCF) for a cluster is introduced to formulate the entropy in the Cluster Variation Method (CVM). As the cluster size increases, the CCF approaches to unity (from below), or −ln(CCF) decreases to zero. The nature of the approximation in the CVM is explained as neglecting the CCF's (or equating them to unity) for clusters larger than the basic cluster of the formulation. For the 2-D square lattice, a hierarchy of entropies for 2 × M ladder-shaped clusters converges to the rigorous entropy as M increases to infinity. The convergence is proved, making use of one coniecture that the decrease of −ln(CCF) to zero as the cluster size increases is monotonic