  The Four Fermi model with discrete chiral symmetry is studied in three
dimensions at non-zero chemical potential and temperature using the Hybrid
Monte Carlo algorithm. The number of fermion flavors is chosen large $(N_f=12)$
to compare with analytic results. A first order chiral symmetry restoring
transition is found at zero temperature with a critical chemical potential
$\mu_c$ in good agreement with the large $N_f$ calculations. The critical index
$\nu$ of the correlation length is measured in good agreement with analytic
calculations. The two dimensional phase diagram (chemical potential vs.
temperature) is mapped out quantitatively. Finite size effects on relatively
small lattices and non-zero fermion mass effects are seen to smooth out the
chiral transition dramatically.
