In this paper we examine a phase transition in $SU(N_{c})$ gauge theories governed by the existence of an infrared fixed point of the renormalization group $beta$ function. The nonlinear integral Schwinger-Dyson equation for a mass function of massless fermions is solved numerically using the exact expression of the running coupling in two-loop approximation for an SU(3) gauge theory. Based on the obtained solution of the Schwinger-Dyson equation, the value of the chiral condensate, $<bar{q}q>$, and the decay constant, $f_{pi}$, of bound states (mesons) are calculated for several values of fermion flavors $N_{f}$. We show that this kind of phase transition is a transition of finite order.
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