Magnetic catalysis effect in (2+1)-dimensional Gross--Neveu model with Zeeman interaction

TL;DR

This paper investigates how Zeeman interaction influences magnetic catalysis and chiral symmetry breaking in a (2+1)-dimensional Gross--Neveu model, revealing that magnetic field orientation and strength significantly affect phase transitions and symmetry restoration.

Contribution

It introduces the effects of Zeeman interaction on magnetic catalysis in the model, showing how it alters phase behavior and symmetry restoration compared to the case without Zeeman interaction.

Findings

Zeeman interaction drastically changes magnetic catalysis effects.

Chiral symmetry can be restored by tilting the magnetic field.

Multiple phases with different magnetic responses are identified.

Abstract

Magnetic catalysis of the chiral symmetry breaking and other magnetic properties of the (2+1)-dimensional Gross--Neveu model are studied taking into account the Zeeman interaction of spin-1/2 quasi-particles (electrons) with tilted (with respect to a system plane) external magnetic field $\vec B=\vec B_\perp+\vec B_\parallel$. The Zeeman interaction is proportional to magnetic moment $\mu_B$ of electrons. For simplicity, temperature and chemical potential are equal to zero throughout the paper. We compare in the framework of the model the above mentioned phenomena both at $\mu_B=0$ and $\mu_B\ne 0$. It is shown that at $\mu_B\ne 0$ the magnetic catalysis effect is drastically changed in comparison with the $\mu_B= 0$ case. Namely, at $\mu_B\ne 0$ the chiral symmetry, being spontaneously broken by $\vec B$ at subcritical coupling constants, is always restored at $|\vec B|\to\infty$ (even at $\vec B_\parallel=0$). Moreover, it is proved in this case that chiral symmetry can be restored simply by tilting $\vec B$ to a system plane, and in the region $ B_\perp\to 0$ the de Haas -- van Alphen oscillations of the magnetization are observed. At supercritical values of coupling constant we have found two chirally non-invariant phases which respond differently on the action of $\vec B$. The first (at rather small values of $|\vec B|$) is a diamagnetic phase, in which there is an enhancement of chiral condensate, whereas the second is a paramagnetic chirally broken phase. Numerical estimates show that phase transitions described in the paper can be achieved at low enough laboratory magnetic fields.