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It was shown recently that a PT-symmetric $i\phi^3$ quantum field theory in$6-\epsilon$ dimensions possesses a nontrivial fixed point. The criticalbehavior of this theory around the fixed point is examined and it is shown thatthe corresponding phase transition is related to the existence of a nontrivialsolution of the gap equation. The theory is studied first in the mean-fieldapproximation and the critical exponents are calculated. Then, it is examinedbeyond 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.

Critical behavior of the PT-symmetric $i\phi^3$ quantum field theory