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
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
].