The Weakly Coupled Gross-Neveu Model with Wilson Fermions

TL;DR

This paper introduces a new analytical approach to study the phase transition in the lattice Gross-Neveu model with Wilson fermions, confirming the existence of an Aoki phase and highlighting parity breaking as the transition mechanism.

Contribution

It develops a novel weak coupling expansion based on partition function zeroes, providing new insights into the phase structure of the model.

Findings

Confirmed the existence of an Aoki phase.

Determined the width of the Aoki phase in weak coupling.

Identified parity breaking as the key mechanism for the phase transition.

Abstract

The nature of the phase transition in the lattice Gross-Neveu model with Wilson fermions is investigated using a new analytical technique. This involves a new type of weak coupling expansion which focuses on the partition function zeroes of the model. Its application to the single flavour Gross-Neveu model yields a phase diagram whose structure is consistent with that predicted from a saddle point approach. The existence of an Aoki phase is confirmed and its width in the weakly coupled region is determined. Parity, rather than chiral symmetry breaking naturally emerges as the driving mechanism for the phase transition.