Renormalization-group flows and fixed points in Yukawa theories

We study renormalization-group flows in Yukawa theories with massless fermions, including determination of fixed points and curves that separate regions of different flow behavior. We assess the reliability of perturbative calculations for various values of Yukawa coupling y and quartic scalar coupling λ by comparing the properties of flows obtained with the beta functions of these couplings calculated to different orders in the loop expansion. The results provide a determination of the region in y and λ where calculations up to two loops can yield reasonably reliable results. In the regime of weak couplings where the perturbative calculations are most reliable, we find that the theories have no nontrivial fixed points, and the flow is toward a free theory in the infrared.