Evaluating and improving the cluster variation method entropy functional for Ising alloys
- National Renewable Energy Laboratory, Golden, CO 80401 (United States)
The success of the {open_quotes}cluster variation method{close_quotes} (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 {ital overestimation} of the exact energy, E, and at the same time, to an {ital underestimation} of {minus}TS, so the free energy F=E{minus}TS is more accurate than either of its parts. This insight explains a problem with {open_quotes}hybrid methods{close_quotes} using MC correlation functions in the CVM entropy expression: They give exact energies E and do not give significantly improved {minus}TS relative to CVM, so they do not benefit from the above noted cancellation of errors. Additionally, hybrid methods suffer from the difficulty of adequately accounting for both ordered and disordered phases in a consistent way. A different technique, the {open_quotes}entropic Monte Carlo{close_quotes} (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 is computationally much less expensive than either MC thermodynamic integration or EMC. {copyright} {ital 1998 American Institute of Physics.}
- OSTI ID:
- 568295
- Journal Information:
- Journal of Chemical Physics, Vol. 108, Issue 7; Other Information: PBD: Feb 1998
- Country of Publication:
- United States
- Language:
- English
Similar Records
Thermodynamical study of the interaction between clusters
Two-sided bounds on the free energy from local states in Monte Carlo simulations