We discuss the phase structure of a lattice Higgs-Yukawa system in the
variational mean field approximation with contributions of fermionic
determinant being calculated in a ladder approximation. In particular,
we demonstrate that in this approximation the ferromagnetic phase in
the Z2 model with naive fermions can appear as an artifact of a finite
lattice and that the phase diagram for this model on infinite lattice
changes qualitatively at space-time dimension D = 4 compared with tho
se at D > 4.