  The quantum-classical crossover from the Fermi liquid towards the Wigner
solid is numerically revisited, considering small square lattice models where
electrons interact via a Coulomb U/r potential. We review a series of exact
numerical results obtained in the presence of weak site disorder for fully
polarized electrons (spinless fermions) and when the spin degrees of freedom
are included. A novel intermediate regime between the Fermi system of weakly
interacting localized particles and the correlated Wigner solid is obtained. A
detailed analysis of the non disordered case shows that the intermediate ground
state is a solid entangled with an excited liquid. For electrons in two
dimensions, this raises the question of the existence of an unnoticed
intermediate liquid-solid phase. Using the Coulomb energy to kinetic energy
ratio r_s ~ U ~ n_s^{-1/2}, we discuss certain analogies between the numerical
results obtained as a function of U for a few particles and the low temperature
behaviors obtained as a function of the carrier density n_s in two dimensional
electron gases. Notably, the new ``exotic state of matter'' numerically
observed at low energies in small clusters occurs at the same intermediate
ratios r_s than the unexpected low temperature metallic behavior characterizing
dilute electron gases. The finite size effects in the limit of strong disorder
are eventually studied in the last section, providing two numerical evidences
that the weak coupling Fermi limit is delimited by a second order quantum phase
transition when one increases U.
