Critical and Tricritical Points for the Massless 2d Gross-Neveu Model Beyond Large N

TL;DR

This paper uses optimized perturbation theory to evaluate the effective potential of the massless 2D Gross-Neveu model at finite temperature and density, including corrections beyond the large-N approximation, and derives analytical expressions for critical and tricritical points.

Contribution

It provides the first analytical calculations of critical and tricritical points with 1/N corrections in the 2D Gross-Neveu model beyond the large-N limit.

Findings

Critical values are smaller than large-N predictions.

Results align with Landau's theorem for phase transitions.

Analytical expressions for tricritical points with 1/N corrections.

Abstract

Using optimized perturbation theory, we evaluate the effective potential for the massless two dimensional Gross-Neveu model at finite temperature and density containing corrections beyond the leading large-N contribution. For large-N, our results exactly reproduce the well known 1/N leading order results for the critical temperature, chemical potential and tricritical points. For finite N, our critical values are smaller than the ones predicted by the large-N approximation and seem to observe Landau's theorem for phase transitions in one space dimension. New analytical results are presented for the tricritical points that include 1/N corrections. The easiness with which the calculations and renormalization are carried out allied to the seemingly convergent optimized results displayed, in this particular application, show the robustness of this method and allows us to obtain neat analytical expressions for the critical as well as tricritical values beyond the results currently known.