Simulation of a free energy upper bound, based on the anticorrelation between an approximate free energy functional and its fluctuation

Journal Article · Fri Oct 01 04:00:00 EDT 1999 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.480050· OSTI ID:686851

Meirovitch, H ^[1]

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1. Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306-4052 (United States)

The local states and hypothetical scanning methods enable one to define a series of lower bound approximations for the free energy, F{sup A} from a sample of configurations simulated by any exact method. F{sup A} is expected to anticorrelate with its fluctuation {sigma}{sup A}, i.e., the better (i.e., larger) is F{sup A} the smaller is {sigma}{sup A}, where {sigma}{sup A} becomes zero for the exact {ital F}. Relying on ideas proposed by Meirovitch and Alexandrowicz [J. Stat. Phys. {bold 15}, 123 (1976)] we best-fit such results to the function F{sup A}=F{sup extp}+C[{sigma}{sup A}]{sup {alpha}} where {ital C}, and {alpha} are parameters to be optimized, and F{sup extp} is the extrapolated value of the free energy. If this function is also convex (concave down), one can obtain an upper bound denoted F{sup up}. This is the intersection of the tangent to the function at the lowest {sigma}{sup A} measured with the vertical axis at {sigma}{sup A}=0. We analyze such simulation data for the square Ising lattice and four polymer chain models for which the correct {ital F} values have been calculated with high precision by exact methods. For all models we have found that the expected concavity always exists and that the results for F{sup extp} and F{sup up} are stable. In particular, extremely accurate results for the free energy and the entropy have been obtained for the Ising model. {copyright} {ital 1999 American Institute of Physics.}

• OSTI ID: 686851
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 16 Vol. 111; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

40 CHEMISTRY
CHAINS
COMPUTERIZED SIMULATION
ENTROPY
FLUCTUATIONS
FREE ENERGY
ISING MODEL
MANY-BODY PROBLEM
POLYMERS
STATISTICAL MECHANICS