The Structure of the Aoki Phase at Weak Coupling

TL;DR

The paper introduces a novel weak coupling expansion method for lattice fermionic theories, enabling perturbative calculation of phase diagrams and providing new insights into the Aoki phase's structure at weak coupling.

Contribution

A new multiplicative weak coupling expansion method is developed to analyze phase diagrams of lattice fermionic theories, specifically applied to the Gross-Neveu model.

Findings

Phase diagram consistent with Aoki's parity symmetry breaking scenario

Quantitative estimates of the Aoki phase width at weak coupling

Validation of the new method through application to the Gross-Neveu model

Abstract

A new method to determine the phase diagram of certain lattice fermionic field theories in the weakly coupled regime is presented. This method involves a new type of weak coupling expansion which is multiplicative rather than additive in nature and allows perturbative calculation of partition function zeroes. Application of the method to the single flavour Gross-Neveu model gives a phase diagram consistent with the parity symmetry breaking scenario of Aoki and provides new quantitative information on the width of the Aoki phase in the weakly coupled sector.