Strongly coupled lattice gauge theory with dynamical fermion mass generation in three dimensions

Abstract

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.

Critical behavior of the (2+1)-dimensional Thirring model

“…In Refs. [29,121] the question has been raised whether for N f = 2 the distinction between χGN and Thirring model might be unimportant and both models might actually coincide. In such a scenario the fixed point pertaining to the χSB phase transition would incidentally lie in a U(4)-symmetric IR attractive subspace of the theory space.…”

“…Exactly the same lattice action employed in the Thirring studies has also been used in simulations of the chiral U(1) ⊗ U(1) Gross-Neveu (χGN) model in three dimensions [121], yielding ν = 0.88 (8) and η * φ = 0.46 (11), probably consistent with the N f = 2 lattice Thirring results ν = 0.85(1), η * φ = 0.65(1) [32] and ν = 0.71(4), η * φ = 0.60(2) [28]. In fact, the symmetry breaking pattern of the lattice Thirring model in the staggered fermion formulation is [29] …”

Analysis of the Lee-Yang zeros in a dynamical mass generation model in three dimensions

“…In order to investigate the chiral properties of the model we concentrate first on two observables: the chiral condensate and the fermion mass [1].…”

“…where A i 's are complex numbers and the exponent s = s(β, κ) [1] describes the finite size scaling of the correlation length. It follows that the real and the imaginary part of the zeros should scale independently with the same exponent.…”

“…Investigating such a lattice model in three dimensions [1] we find three regions in the β−κ plane with possibly different critical behaviour in the chiral limit of the model. These three regions are presented in Fig.(1).…”