  We present new results of our ongoing project on the investigation of the
phase structure of the Higgs-Yukawa model at small and large bare Yukawa
couplings. The critical exponents of the second order bulk phase transitions of
this model are determined from finite-size analyses and compared to the pure
O(4)-model to test for triviality and the possibility of having a non-Gaussian
fixed point. In addition, we will present a first study of Higgs boson masses
and fermion correlation functions.
