  The impact of leading collective electronic fluctuations on a free energy of
a prototype 1D model for molecular systems is considered within the recently
developed Fluctuating Local Field (FLF) approach. The FLF method is a
non-perturbative extension of a mean-field theory, where a self-consistent
effective constant field is replaced by a fluctuating one. Integrating the
fluctuating field out numerically exactly allows to account for collective
electronic fluctuations mediated by this field without any assumptions on their
magnitude, degree of nonlinearity, etc. Using a half-filled Hubbard ring as a
benchmark system, we find that the FLF method noticeably improves a mean-field
estimation for the free energy, in particular below the mean-field Ne\'el
temperature. We further demonstrate that the mean-field result can be even more
improved introducing a multi-mode FLF scheme that additionally takes into
account sub-leading fluctuations. Possible applications for the thermodynamics
of real molecules are also discussed.
