Thermodynamic instabilities in nonlocal NJL models

TL;DR

This paper investigates thermodynamic instabilities in nonlocal NJL models, linking them to the analytical structure of quark propagator poles and exploring how the Polyakov loop influences these instabilities.

Contribution

It reveals the connection between thermodynamic instabilities and unstable poles in the quark propagator, and analyzes the impact of the Polyakov loop on these phenomena.

Findings

Thermodynamic instabilities are associated with highly unstable poles in the quark propagator.

Different regulators influence the presence and nature of these instabilities.

Including the Polyakov loop softens the instabilities by affecting the propagator's poles.

Abstract

It has been recently pointed out, that nonlocal Nambu--Jona-Lasinio models, may present unphysical thermodynamical behavior like negative pressure and oscillating entropy. Here we show how these thermodynamic instabilities can be related to the analytical structure of the poles of the quark propagator in the model. The analysis is carried out for two different regulators and we show, in each case, how the instabilities are related to the pressence of highly unstable poles. We also argue that the softening of these instabilities by the inclusion of the Polyakov loop is related to the effect the latter has on the poles of the propagator.