STUDY OF THE ASYMPTOTIC FREEDOM OF 2D YUKAWA MODELS ON THE LATTICE

We investigate on the lattice the Yukawa models in 2 dimensions with Z (2) and U(1) symmetries. These models reduce to the usual and chiral G ross-Neveu models, respectively, when the kinetic and the self-couplin g terms of the scalar field are turned off. The numerical data and mea n field arguments suggest that, at least for some range of the scalar field hopping parameter, fermion mass is dynamically generated for arb itrarily weak Yukawa coupling. The models are asymptotically free in t his coupling, like the Gross-Neveu models, even when the scalar quarti c self-coupling is strong.