Yukawa coupling in three dimensions. II

The effective potential for the simplest Yukawa model in 2 + 1 dimensions discussed in a previous paper is computed to two-loop order. The radiative corrections serve to destabilize the vacuum, both when the fermion is a Dirac Spinor and when it is a Majorana spinor but with the instability occurring at values of the external held where perturbation theory is unreliable. If the Yukawa coupling and the self-coupling of the scaler are related by supersymmetry, stability is present. Renormalization of the supersymmetric version of this model presents special difficulties when the auxiliary held is not eliminated using the field equations. In a;;appendix, the renormalization group functions for a three dimensional Euclidean space model with two Yukawa couplings is analyzed, showing that one of the two couplings is asymptotically free. [S0556-2821(99)08018-2].