Infrared asymptotic freedom for the pseudoscalar Yukawa model at the critical point

We consider the pseudoscalar Yukawa model on a four dimensional Euclidean lattice. The fermions are integrated out giving an effective boson interaction. We show that for weak coupling this interaction is in the class covered by the Gawedzki-Kupiainen renormalization group analysis. It follows that one can adjust parameters so that the flow of the renormalization group is toward a free massless boson theory. This establishes the existence of the critical theory and controls its long distance behavior.