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

Authors
Citation
H. Meirovitch, Simulation of a free energy upper bound, based on the anticorrelation between an approximate free energy functional and its fluctuation, J CHEM PHYS, 111(16), 1999, pp. 7215-7224
Citations number
31
Categorie Soggetti
Physical Chemistry/Chemical Physics
Journal title
JOURNAL OF CHEMICAL PHYSICS
ISSN journal
00219606 → ACNP
Volume
111
Issue
16
Year of publication
1999
Pages
7215 - 7224
Database
ISI
SICI code
0021-9606(19991022)111:16<7215:SOAFEU>2.0.ZU;2-A
Abstract
The local states and hypothetical scanning methods enable one to define a s eries of lower bound approximations for the free energy, F-A from a sample of configurations simulated by any exact method. F-A is expected to anticor relate with its fluctuation sigma(A), i.e., the better (i.e., larger) is F- A the smaller is sigma(A), where sigma(A) becomes zero for the exact F. Rel ying on ideas proposed by Meirovitch and Alexandrowicz [J. Stat. Phys. 15, 123 (1976)] we best-fit such results to the function F-A = F-extp + C[sigma (A)](alpha) where C, and alpha are parameters to be optimized, and F-extp i s the extrapolated value of the free energy. If this function is also conve x (concave down), one can obtain an upper bound denoted F-up. This is the i ntersection of the tangent to the function at the lowest sigma(A) measured with the vertical axis at sigma(A) = 0. We analyze such simulation data for the square Ising lattice and four polymer chain models for which the corre ct 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-extp and F-up are stable. In particular, extremely accur ate results for the free energy and the entropy have been obtained for the Ising model. (C) 1999 American Institute of Physics. [S0021-9606(99)50640-5 ].