  We describe the chiral phase transition for vector-like SU(N) gauge theories
as a function of the number of quark flavors Nf by making use of an
anomaly-induced effective potential. The potential depends explicitly on the
full beta-function and the anomalous dimension \gamma of the quark mass
operator. By using this potential we argue that chiral symmetry is restored for
\gamma <1. A perturbative computation of \gamma then leads to an estimate of
the critical value Nf^c for the transition.
