  The exact analytic solutions of the linearized Schwinger-Dyson equation of
fermion self-energy are used to obtain the effective four-fermion and gauge
coupling criticality curves for dynamical chiral symmetry breaking. The results
show that when the zero-momentum gauge coupling $\alpha(0) < \alpha_0(0)$, the
critical gauge coupling in the pure gauge interaction case, the minimal
critical four-fermion coupling $\beta_{\rm min}$ is always non-zero and
positive and will go up as the $\alpha(0)$ decreases. The use of the exact
solutions also allow us to make quite definite estimations of the momentum
scales where chiral symmetry breaking would happen if the values of an infrared
parameter $\xi$ are given separately.
