1 How much are 2d Yukawa models similar to the Gross-Neveu models? ∗

We present numerical evidence that the 2d Yukawa models with strong quartic selfcoupling of the scalar field have the same phase structure and are asymptotically free in the Yukawa coupling like the Gross-Neveu models. 1. Yukawa models in 2 dimensions The 2d Yukawa models (Y2) with chiral Z(2) or U(1) symmetries are natural extensions of the usual or chiral 2d Gross-Neveu (GN) models, respectively. Starting from the auxiliary field representation of the 4-fermion coupling, one can add both the kinetic term and a self-interaction of this field φ into the GN action. On the lattice the Z(2) symmetric Y2 action is then (we introduce NF/4 “naive ” Dirac fermion fields ψα) S = −2κ ∑ φxφx+µ + ∑ φ 2 x + λ ∑ x,α x,µ ψ α x ∂/ψα x + y x,α x ψ α x φxψ α x x (φ 2 x − 1) 2