Study of the Asymptotic Freedom of 2D Yukawa Models on the Lattice

TL;DR

This paper explores 2D lattice Yukawa models with Z(2) and U(1) symmetries, demonstrating that they exhibit asymptotic freedom and dynamical fermion mass generation similar to Gross-Neveu models, even with strong scalar self-coupling.

Contribution

It provides numerical and mean field evidence that 2D Yukawa models are asymptotically free and can generate fermion mass dynamically at weak coupling, extending understanding of these models.

Findings

Fermion mass is dynamically generated at weak Yukawa coupling.

Models are asymptotically free even with strong scalar self-coupling.

Numerical data supports the asymptotic freedom and mass generation phenomena.

Abstract

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 Gross-Neveu models, respectively, when the kinetic and the selfcoupling terms of the scalar field are turned off. The numerical data and mean field arguments suggest that, at least for some range of the scalar field hopping parameter, fermion mass is dynamically generated for arbitrarily weak Yukawa coupling. The models are asymptotically free in this coupling, like the Gross-Neveu models, even when the scalar quartic selfcoupling is strong.