Multicritical Points in a Lattice Yukawa Model with the Wilson-Yukawa Coupling

TL;DR

This paper analytically investigates the phase structure of a lattice chiral-invariant fermion-scalar model with Yukawa couplings, identifying a multicritical line where four phases meet, supported by Monte Carlo simulations.

Contribution

It provides an analytical derivation of the multicritical line in the phase diagram of a lattice Yukawa model, complementing previous numerical studies.

Findings

Identification of a multicritical line where four phases meet

Good agreement between analytical results and Monte Carlo simulations

Use of effective scalar model and mean-field method for analysis

Abstract

For a lattice regularized chiral-invariant $SU(2)_L\times~SU(2)_R$ fermion-scalar model with a Yukawa coupling $y$ and a Wilson-Yukawa coupling $w$, we investigate the phase structure and in particular show the existence of the multicritical line, in the strong Yukawa and/or Wilson Yukawa coupling region, at which four phases meet. The result is in good agreement with the Monte Carlo simulation. This analytical result is derived from the effective scalar model obtained by integrating out the fermion field where the action is explicitly obtained from the hopping parameter expansion up to next-to-leading order. For estimates on the correlation function of the scalar field we apply the mean-field method.