Exact tricritical point from next-to-leading-order stability analysis

TL;DR

This paper extends stability analysis to higher order perturbation theory in the massive chiral Gross-Neveu model, allowing exact determination of the tricritical point without full numerical calculations.

Contribution

It introduces a higher order perturbative stability analysis to precisely locate the tricritical point in the phase diagram.

Findings

Exact location of the tricritical point achieved

Higher order stability analysis extends previous methods

Spectral gap divergences managed with many-body theory tools

Abstract

In the massive chiral Gross-Neveu model, a phase boundary separates a homogeneous from an inhomogeneous phase. It consists of two parts, a second order line and a first order line, joined at a tricritical point. Whereas the first order phase boundary requires a full, numerical Hartree-Fock calculation, the second order phase boundary can be determined exactly and with less effort by a perturbative stability analysis. We extend this stability analysis to higher order perturbation theory. This enables us to locate the tricritical point exactly, without need to perform a Hartree-Fock calculation. Divergencies due to the emergence of spectral gaps in a spatially periodic perturbation are handled using well established tools from many body theory.