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

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.

v3;14 pages; 8 figures;minor changes of the text;published version

References in corpus (17)

• The electronic properties of graphene
• Superconductivity at 38 K in the iron arsenide (Ba1-xKx)Fe2As2
• Excitonic gap, phase transition, and quantum Hall effect in graphene
• Color-flavor locked superconductor in a magnetic field
• Color superconducting matter in a magnetic field
• Emergence of Tricritical Point and Liquid-Gas Phase in the Massless 2+1 Dimensional Gross-Neveu Model
• Dynamically Induced Zeeman Effect in Massless QED
• Dynamically Generated Anomalous Magnetic Moment in Massless QED
• Updating the Phase Diagram of the Gross-Neveu Model in 2+1 Dimensions
• Magnetization of Planar Four-Fermion Systems
• Phase diagram of the magnetized planar Gross-Neveu model beyond the large-N approximation
• Nonlinear magnetization of graphene
• Phase diagram of quark-antiquark and diquark condensates at finite temperature and density in the 3-dimensional Gross Neveu model
• Chiral phase transition in a planar four-Fermi model in a tilted magnetic field
• Phase transition in the 3-D massive Gross-Neveu model
• Renormalization flow towards gravitational catalysis in the 3d Gross-Neveu model
• Phase diagram of quark-antiquark and diquark condensates in the 3-dimensional Gross Neveu model with the 4-component spinor representation

Cited by in corpus (12)

• Chiral Symmetry Breaking and the Quantum Hall Effect in Monolayer Graphene
• Phase transitions in hexagonal, graphene-like lattice sheets and nanotubes under the influence of external conditions
• Tilted Dirac cone effects and chiral symmetry breaking in a planar four-fermion model
• Interplay between superconductivity and chiral symmetry breaking in a (2+1)-dimensional model with compactified spatial coordinate
• Magnetic Field Effect in the Fine-Structure Constant and Electron Dynamical Mass
• Superconducting phase transition in planar fermionic models with Dirac cone tilting
• The magnetized (2+1)-dimensional Gross-Neveu model at finite density
• First order phase transitions within Weyl type of materials at low temperatures
• Broken symmetry states in bilayer graphene in electric and in-plane magnetic fields
• Testing the equivalence between the planar Gross-Neveu and Thirring models at $N=1$
• Fate of chiral symmetry in Riemann-Cartan geometry
• Dense Baryonic Matter and Applications of QCD Phase Diagram Dualities