Stability of homogeneous chiral phases against inhomogeneous perturbations in 2+1 dimensions

TL;DR

This paper investigates the stability of homogeneous chiral phases in 2+1 dimensional models, finding they are stable against inhomogeneous perturbations across various conditions, with analytic results at zero temperature.

Contribution

It provides a comprehensive analysis of inhomogeneous phases in multiple models, demonstrating the robustness of homogeneous phases in 2+1 dimensions.

Findings

Homogeneous phases are stable against inhomogeneous perturbations.

No evidence of inhomogeneous phases in studied models.

Analytic results obtained at zero temperature.

Abstract

In this work, inhomogeneous chiral phases are studied in a variety of Four-Fermion and Yukawa models in $2+1$ dimensions at zero and non-zero temperature and chemical potentials. Employing the mean-field approximation, we do not find indications for an inhomogeneous phase in any of the studied models. We show that the homogeneous phases are stable against inhomogeneous perturbations. At zero temperature, full analytic results are presented.