  It was shown recently that a PT-symmetric $i\phi^3$ quantum field theory in
$6-\epsilon$ dimensions possesses a nontrivial fixed point. The critical
behavior of this theory around the fixed point is examined and it is shown that
the corresponding phase transition is related to the existence of a nontrivial
solution of the gap equation. The theory is studied first in the mean-field
approximation and the critical exponents are calculated. Then, it is examined
beyond the mean-field approximation by using renormalization-group techniques,
and the critical exponents for $6-\epsilon$ dimensions are calculated to order
$\epsilon$. It is shown that because of its stability the PT-symmetric
$i\phi^3$ theory has a higher predictive power than the conventional $\phi^3$
theory. A comparison of the $i\phi^3$ model with the Lee-Yang model is given.
