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

We develop analytical technique for examining phase structure of $Z_2$, $U(1)$, and $SU(2)$ lattice Higgs-Yukawa systems with radially frozen Higgs fields and chirally invariant lattice fermion actions. The method is based on variational mean field approximation. We analyse phase diagrams of such systems with different forms of lattice fermion actions and demonstrate that it crucially depends both on the symmetry group and on the form of the action. We discuss location in the diagrams of possible non-trivial fixed points relevant to continuum physics, and argue that the candidates can exist only in $Z_2$ system with SLAC action and $U(1)$ systems with naive and SLAC actions. [Note: By a product, missing term in Eq. (3.5) of hep-lat/9309010 is reconstructed, that, however, affects only the result of Sect. 4.3 (Fig. 3) of that reference (cf. Fig. 2(c) of this paper).]