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

¹ Institute for High Energy Physics, 142281, Protvino, Moscow Region, Russia
² University “Dubna” (Protvino branch), 142281, Protvino, Moscow Region, Russia

Published online: 29 May 2015

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 $$\overrightarrow{B}={\overrightarrow{B}}_{\perp }+{\overrightarrow{B}}_{\parallel }$$. The Zeeman interaction is proportional to magnetic moment μ_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 μ_B = 0 and μ_B ≠ 0. It is shown that at μ_B ≠ 0 the magnetic catalysis effect is drastically changed in comparison with the μ_B = 0 case. Namely, at μ_B ≠ 0 the chiral symmetry, being spontaneously broken by $$\overrightarrow{B}$$ at subcritical coupling constants, is always restored at |$$\overrightarrow{B}$$| → ∞ (even at $${\overrightarrow{B}}_{\parallel }$$ = 0). Moreover, it is proved in this case that chiral symmetry can be restored simply by tilting $$\overrightarrow{B}$$ to a system plane, and in the region B_⊥ → 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 $$\overrightarrow{B}$$. The first (at rather small values of |$$\overrightarrow{B}$$|) 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.