Magnetic Catalysis and Oscillating Effects in Nambu -- Jona-Lasinio Model at Nonzero Chemical Potential

TL;DR

This paper explores the phase structure of the Nambu-Jona-Lasinio model under nonzero chemical potential, revealing complex phase diagrams with multiple phases, oscillating physical parameters, and various phase transitions in different space-time settings.

Contribution

It provides a detailed analysis of the phase structure and oscillating effects in the NJL model at nonzero chemical potential, including the discovery of infinitely many phases and tricritical points.

Findings

Existence of infinitely many massless and massive phases.

Oscillations in magnetization, pressure, and condensates at large system size or weak magnetic field.

Presence of first and second order phase transitions with tricritical points.

Abstract

Phase structure of the four dimensional Nambu -- Jona-Lasinio model has been investigated in two cases: 1) in nonsimply connected space-time of the form $R^3\times S^1$ (space coordinate is compactified and the length of the circle $S^1$ is $L$) with nonzero chemical potential $\mu$ and 2) in Minkowski space-time at nonzero values of $\mu,H$, where $H$ is the external magnetic field. In both cases on phase portraits of the model there are infinitly many massless chirally symmetric phases as well as massive ones with spontaneously broken chiral invariance. Such phase structure leads unavoidably to oscillations of some physical parameters at $L\to\infty$ or $H\to 0$, including magnetization, pressure and particle density of the system as well as quark condensate and critical curve of chiral phase transitions. Phase transitions of 1st and 2nd orders and several tricritical points have been shown to exist on phase diagrams of the model.