EVALUATING AND IMPROVING THE CLUSTER VARIATION METHOD ENTROPY FUNCTIONAL FOR ISING ALLOYS

The success of the ''cluster variation method'' (CVM) in reproducing q uite accurately the free energies of Monte Carlo (MC) calculations on Ising models is explained in terms of identifying a cancellation of er rors: We show that the CVM produces correlation functions that are too close to zero, which leads to an overestimation of the exact energy, E, and at the same time, to an underestimation of - TS, so the free en ergy F= E - TS is more accurate than either of its parts. This insight explains a problem with ''hybrid methods'' using MC correlation funct ions in the CVM entropy expression: They give exact energies E and do not give significantly improved -TS relative to CVM, so they do nor be nefit from the above noted cancellation of errors. Additionally, hybri d methods suffer from the difficulty of adequately accounting for both ordered and disordered phases in a consistent way. A different techni que, the ''entropic Monte Carlo'' (EMC), is shown here to provide a me ans for critically evaluating the CVM entropy. Inspired by EMC results , we find a universal and simple correlation to the CVM entropy which produces individual components of the free energy with MC accuracy, bu t is computationally much less expensive than either MC thermodynamic integration or EMC. (C) 1998 American Institute of Physics.