Phase structure of Higgs-Yukawa systems with chirally invariant lattice fermion actions

We develop an analytical technique for examining the phase structure of ${\mathit{Z}}_2$, U(1), and SU(2) lattice Higgs-Yukawa systems with radially frozen Higgs fields and chirally invariant lattice fermion actions. The method is based on the variational mean-field approximation. We analyze the phase diagrams of such systems with different forms of lattice fermion action and demonstrate that they depend crucially both on the symmetry group and on the form of the action. We discuss the location in the diagrams of possible nontrivial fixed points relevant to continuum physics and argue that such points can exist only in the ${\mathit{Z}}_2$ system with the SLAC action and in the U(1) systems with the naive or SLAC action.