  Thermal-equilibrated finite classical lattices are considered as a minimal
model of the systems showing an interplay between low energy collective
fluctuations and single site degrees of freedom. Standard local field approach,
as well as classical limit of the bosonic DMFT method, do not provide a
satisfactory description of Ising and Heisenberg small lattices subjected to an
external polarizing field. We show that a dramatic improvement can be achieved
within a simple approach, in which the local field appears to be a fluctuating
quantity related to the low energy degree(s) of freedom.
