Phase structure of a three-dimensional Yukawa model

We use the method of the exact renormalization group to study the renormalization group flows of an O(N) invariant Yukawa model in three dimensional Euclidean space consisting of one real scalar and N real spinor fields. We obtain a phase structure similar to that of the N-vector model with cubic anisotropy, possessing a region of parameters exhibiting a first order transition. The particular case with one real fermion (N=1) belongs to the same universality class as the Wess-Zumino model with one supersymmetry. For the critical exponents of the Wilson-Fisher type fixed points, our 1-loop approximations are generally consistent with the results of previous studies.