Thermodynamics of the Massive Gross-Neveu Model

TL;DR

This paper analyzes the thermodynamics of massive Gross-Neveu models at finite temperature and density, revealing phase transition lines and tricritical points, with implications for understanding chiral transitions in QCD.

Contribution

It provides an analytical study of massive Gross-Neveu models, highlighting phase transition behaviors and thermodynamic properties relevant to higher-dimensional QCD.

Findings

Lines of first order phase transitions at finite densities

Presence of tricritical points for small fermion masses

Properties of pion-like states in models with broken continuous chiral symmetry

Abstract

We study the thermodynamics of massive Gross-Neveu models with explicitly broken discrete or continuous chiral symmetries for finite temperature and fermion densities. The large $N$ limit is discussed bearing attention to the no-go theorems for symmetry breaking in two dimensions which apply to the massless cases. The main purpose of the study is to serve as analytical orientation for the more complex problem of chiral transition in $4-$dimensional QCD with quarks. For any non-vanishing fermion mass we find, at finite densities, lines of first order phase transitions. For small mass values traces of would-be second order transitions and a tricritical point are recognizable. We study the thermodynamics of these models, and in the model with broken continuous chiral symmetry we examine the properties of the pion like state.