Functional renormalization group study of the Nambu--Jona-Lasinio model at finite temperature and density in an external magnetic field

TL;DR

This paper uses the functional renormalization group to explore how an external magnetic field influences the phase structure of the Nambu--Jona-Lasinio model at finite temperature and density, revealing oscillatory behavior and complex phase boundaries.

Contribution

It provides a detailed analysis of the UV fixed point behavior and phase diagram modifications under magnetic fields, a novel application of the FRG to the NJL model in these conditions.

Findings

UV fixed point oscillates with magnetic field at low temperature and finite density

Phase boundaries exhibit non-monotonic movement with increasing magnetic field

Identifies de Haas--van Alphen oscillations in the phase structure

Abstract

In this study, we investigate the Nambu--Jona-Lasinio (NJL) model at finite temperature and finite density in an external magnetic field using the functional renormalization group. We investigate the dependence of the position of the ultraviolet fixed point (UVFP) of the four-Fermi coupling constant on the temperature, density, and external magnetic field, and we obtain the chiral phase structure. The UVFP at low temperature and finite chemical potential oscillates in a small external magnetic field, which can be interpreted as the de Haas--van Alphen effect. We also obtain phase diagrams with complex structures, where the phase boundary moves back and forth as the external magnetic field increases in the low temperature and high density region.