K. G. Klimenko, R. N. Zhokhov
Magnetic catalysis of 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 quasiparticles (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 a magnetic moment of electrons, i.e. to Bohr magneton $\mu_B$. For simplicity, temperature and chemical potential are equal to zero throughout the paper. In the framework of the model we compare 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, the chiral symmetry, being spontaneously broken by $\vec B$ at under-critical coupling constants, %or enhanced at rather small values of $|\vec B|$, is always restored at $|\vec B|\to\infty$ (even at $\vec B_\parallel=0$). Moreover, it is proved that chiral symmetry can be restored simply by tilting $\vec B$ to a system plane. In this case, 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.
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http://arxiv.org/abs/1307.7265
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