The influence of magnetic field on the pion superfluidity and phase structure in the NJL model

TL;DR

This paper investigates how external magnetic fields affect pion superfluidity and phase transitions within the NJL model, revealing complex behaviors and shifts in critical points due to magnetic influence.

Contribution

It provides a detailed analysis of magnetic field effects on pion superfluidity and phase structure in the NJL model, including the movement of the tricritical point.

Findings

Magnetic field causes non-monotonic effects on pion condensate.

Tricritical point shifts to lower isospin chemical potential and higher temperature with stronger magnetic fields.

Magnetic field influences the chiral condensate in a significant way.

Abstract

The influence of the magnetic field on the pion superfluidity and the phase structure is analyzed in the framework of the two-flavor Nambu--Jona-Lasinio(NJL) model. To do this, we first derive the thermodynamic potential from the Lagrangian density of the NJL model in the mean field approximation. Using this thermodynamic potential, we get the gap equation of the chiral condensate and the pion condensate. The effect of external magnetic field on the pion condensate is not simple promotion or suppression, which we will discuss in detail in the paper. It is shown that the tricritical point on the pion superfluidity phase transition line moves to the space with smaller isospin chemical potential and higher temperature when the external magnetic field becomes stronger. The influence of external magnetic field on the chiral condensate is also studied.