We investigate the critical behaviour of a three-dimensional lattice χU φ 3 model in the chiral limit. The model consists of a staggered fermion field, a U (1) gauge field (with coupling parameter β) and a complex scalar field (with hopping parameter κ). Two different methods are used: 1) fits of the chiral condensate and the mass of the neutral unconfined composite fermion to an equation of state and 2) finite size scaling investigations of the Lee-Yang zeros of the partition function in the complex fermion mass plane. For strong gauge coupling (β < 1) the critical exponents for the chiral phase transition are determined. We find strong indications that the chiral phase transition is in one universality class in this β interval: that of the three-dimensional Gross-Neveu model with two fermions. Thus the continuum limit of the χU φ 3 model defines here a nonperturbatively renormalizable gauge theory with dynamical mass generation. At weak gauge coupling and small κ, we explore a region in which the mass in the neutral fermion channel is large but the chiral condensate on finite lattices very small. If it does not vanish in the infinite volume limit, then a continuum limit with massive unconfined fermion might be possible in this region, too.

We investigate a strongly U(1) gauge theory with fermions and scalars on a three dimensional lattice and analyze whether the continuum limit might be a renormalizable theory with dynamical mass generation. Most attention is paid to the weak coupling region where a possible new dynamical mass generation mechanism might exist. There we investigate the mass of the composite fermion, the chiral condensate and the scaling of the Lee-Yang zeros.

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