  We discuss the non-thermal phase structure of a chirally invariant
Higgs-Yukawa model on the lattice in the presence of a higher dimensional
$\Phi^6$-term. For the exploration of the phase diagram we use analytical,
lattice perturbative calculations of the constraint effectice potential as well
as numerical simulations. We also present first results of the effects of the
$\Phi^6$-term on the lower Higgs boson mass bounds.
