Evaluating and Improving the Cluster Variation Method Entropy Functional for Ising Alloys

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The success of the 'cluster variation method' (CVM) in reproducing quite accurately the free energies of Monte Carlo (MC) calculations on Ising models is explained in terms of identifying a cancellation of errors: We show that the CVM produces correlation functions that are too close to zero, which leads to an overestimation of exact energy, E, and at the same time, to an underestimation of -TS,so the free energy F=E - TS is more accurate than either of its parts. This insight explains a problem with 'hybrid methods' using MC correlation functions in the CVM entropy expression: They give exact energyes E and do not give significantly improved - TS relative to FCVM, so they do not benefit from the above noted cancellation of errors. Additionally, hybrid methods suffer from thedifficulty of adequately accounting for both ordered and disordered phases in a consistent way. A different technique, the 'entropic Monte Carlo' (EMC), is shown here to provide a means 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, but iscomputationally much less expensive than either MC thermodynamic integration or EMC.
Original languageAmerican English
Pages (from-to)2912-2918
Number of pages7
JournalThe Journal of Chemical Physics
Issue number7
StatePublished - 1998

NREL Publication Number

  • NREL/JA-590-24388


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