Emergence of Tricritical Point and Liquid-Gas Phase in the Massless 2+1 Dimensional Gross-Neveu Model

TL;DR

This paper uses optimized perturbation theory to analyze the 2+1 dimensional massless Gross-Neveu model, revealing a tricritical point and a liquid-gas phase transition, and providing analytical expressions for key physical quantities.

Contribution

It introduces a non-perturbative analysis of the model, identifying a tricritical point and a liquid-gas phase, extending beyond previous large-N results.

Findings

Identification of a tricritical point in the phase diagram.

Discovery of a liquid-gas phase transition in the model.

Derivation of N-dependent analytical expressions for physical quantities.

Abstract

A complete thermodynamical analysis of the 2+1 dimensional massless Gross-Neveu model is performed using the optimized perturbation theory. This is a non-perturbative method that allows us to go beyond the known large-N results already at lowest order. Our results, for a finite number of fermion species, N, show the existence of a tricritical point in the temperature and chemical potential phase diagram for discrete chiral phase transition allowing us to precisely to locate it. By studying the phase diagram in the pressure and inverse density plane, we also show the existence of a liquid-gas phase, which, so far, was unknown to exist in this model. Finally, we also derive N dependent analytical expressions for the fermionic mass, critical temperature and critical chemical potential.