Phase transition in the 3-D massive Gross-Neveu model

TL;DR

This paper investigates the 3D massive Gross-Neveu model at finite temperature, deriving a renormalized four-point function and analyzing the free energy to identify a second-order phase transition.

Contribution

It provides a closed-form expression for the renormalized T-dependent four-point function and demonstrates the existence of a second-order phase transition in the model.

Findings

Identification of a singularity indicating a phase transition

Derivation of T-dependent mass that vanishes at critical temperature

Confirmation of a second-order phase transition in the model

Abstract

We consider the 3-dimensional massive Gross-Neveu model at finite temperature as an effective theory for strong interactions. Using the Matsubara imaginary time formalism, we derive a closed form for the renormalized $T$-dependent four-point function. This gives a singularity, suggesting a phase transition. Considering the free energy we obtain the $T$-dependent mass, which goes to zero for some temperature. These results lead us to the conclusion that there is a second-order phase transition.