Phase diagram of quark-antiquark and diquark condensates in the 3-dimensional Gross Neveu model with the 4-component spinor representation

TL;DR

This paper maps the phase diagram of quark-antiquark and diquark condensates in a 3D Gross Neveu model with 4-component quarks, revealing a coexisting phase absent in 2-component cases, and drawing parallels to the 4D Nambu Jona-Lasinio model.

Contribution

It demonstrates the existence of a coexisting phase of condensates in the 3D GN model with 4-component quarks, highlighting its similarity to the 4D NJL model and contrasting with 2-component quark cases.

Findings

Coexisting phase of condensates appears in 3D GN with 4-component quarks.

The phase diagram differs from 2-component quark models.

The 3D GN model with 4-component quarks resembles the 4D NJL model.

Abstract

We construct the phase diagram of the quark-antiquark and diquark condensates at finite temperature and density in the 2 + 1 dimensional (3D) two flavor massless Gross Neveu (GN) model with the 4-component quarks. In contrast to the case of the 2-component quarks, there appears the coexisting phase of the quark-antiquark and diquark condensates. This is the crucial difference between the 2-component and 4-component quark cases in the 3D GN model. The coexisting phase is also seen in the 4D Nambu Jona-Lasinio model. Then we see that the 3D GN model with the 4-component quarks bears closer resemblance to the 4D Nambu Jona-Lasinio model.