Approach to D-dimensional Gross-Neveu model at finite temperature and curvature

TL;DR

This paper investigates the phase structure of the D-dimensional Gross-Neveu model at finite temperature, density, and curvature, revealing a third order critical line similar to the two-dimensional case.

Contribution

It extends the analysis of the Gross-Neveu model to higher dimensions with finite temperature, density, and curvature, using effective potential calculations in a weak background and large-N approximation.

Findings

Identification of a third order critical line in the phase diagram

Extension of phase structure analysis to D=2 and D=3 dimensions

Use of weak background approximation and 1/N expansion methods

Abstract

We discuss phase structure of chiral symmetry breaking of the $D$-dimensional ($2\leq D\leq3$) Gross-Neveu model at finite temperature, density and constant curvature. We evaluate the effective potential in a weak background approximation to thermalize the model as well as in the leading order of the $1/N$-expansion. A third order critical line is observed similarly to the $D=2$ case.