  The phase diagram of a chirally invariant lattice Higgs-Yukawa model is
explored by means of numerical simulations. The results revealing a rich phase
structure are compared to analytical large Nf calculations which we performed
earlier. The analytical and numerical results are in excellent agreement at
large values of Nf. In the opposite case the large Nf computation still gives a
good qualitative description of the phase diagram. In particular we find
numerical evidence for the predicted ferrimagnetic phase at intermediate values
of the Yukawa coupling constant and for the symmetric phase at strong Yukawa
couplings. Emphasis is put on the finite size effects which can hide the
existence of the latter symmetric phase.
