  We applied a mean-field approach associated to Monte Carlo simulations in
order to study the spin-1 ferromagnetic Blume-Capel model in the square and the
linear lattice. This new technique, which we call MFT-MC, determines the
molecular field as the magnetization response of a Monte Carlo simulation. The
resulting phase diagram is qualitatively correct, in contrast to
effective-field approximations, in which the first-order line is not
perpendicular to the anisotropy axis at low temperatures. Thermodynamic
quantities, as the entropy and the specific heat curves can be obtained so as
to analyze the nature of the phase transition points. Also, the possibility of
using larger sizes constitutes an improvement regarding other mean-field
approximations that use clusters.
