  The phase diagram of the spin-3/2 Blume-Capel model in two dimensions is
explored by conventional finite-size scaling, conformal invariance and Monte
Carlo simulations. The model in its $\tau$-continuum Hamiltonian version is
also considered and compared with others spin-3/2 quantum chains. Our results
indicate that differently from the standard spin-1 Blume-Capel model there is
no multicritical point along the order-disorder transition line. This is in
qualitative agreement with mean field prediction but in disagreement with
previous approximate renormalization group calculations. We also presented new
results for the spin-1 Blume-Capel model.
