Renormalization Group Study of Magnetic Catalysis in the 3d Gross-Neveu Model

Abstract

Magnetic catalysis describes the enhancement of symmetry breaking quantum fluctuations in chirally symmetric quantum field theories by the coupling of fermionic degrees of freedom to a magnetic background configuration. We use the functional renormalization group to investigate this phenomenon for interacting Dirac fermions propagating in (2+1)-dimensional spacetime, described by the Gross-Neveu model. We identify pointlike operators up to quartic fermionic terms that can be generated in the renormalization group flow by the presence of an external magnetic field. We employ the beta function for the fermionic coupling to quantitatively analyze the field dependence of the induced spectral gap. Within our pointlike truncation, the renormalization group flow provides a simple picture for magnetic catalysis.

14 pages, 6 figures, typos corrected

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Cited by in corpus (38)

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• Deconfinement transition in two-flavour lattice QCD with dynamical overlap fermions in an external magnetic field
• Spontaneous generation of local CP violation and inverse magnetic catalysis
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• Inverse Magnetic Catalysis in the Soft-Wall Model of AdS/QCD
• Ising and Gross-Neveu model in next-to-leading order
• Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
• Heavy meson spectroscopy under strong magnetic field
• Inverse Magnetic Catalysis in the three-flavor NJL model with axial-vector interaction
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• Surface Magnetic Catalysis
• A curvature bound from gravitational catalysis
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• The quark-hadron thermodynamics in magnetic field
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• Impacts of (inverse) magnetic catalysis on screening masses of neutral pions and sigma mesons in hot and magnetized quark matter
• Momentum dependence of quantum critical Dirac systems
• Local potential approximation for the renormalization group flow of fermionic field theories
• Inhomogeneous phases in the chirally imbalanced $2+1$-dimensional Gross-Neveu model and their absence in the continuum limit
• Possible formation of high temperature superconductor at early stage of heavy-ion collisions
• Lattice investigation of an inhomogeneous phase of the 2+1-dimensional Gross-Neveu model in the limit of infinitely many flavors
• Magnetic catalysis effect in (2+1)-dimensional Gross--Neveu model with Zeeman interaction
• Four-fermion interactions and the chiral symmetry breaking in an external magnetic field
• Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model
• Renormalization flow towards gravitational catalysis in the 3d Gross-Neveu model
• Functional renormalization group study of the Nambu--Jona-Lasinio model at finite temperature and density in an external magnetic field
• Critical Wess-Zumino models with four supercharges from the functional renormalization group
• Phase diagram of the 2+1-dimensional Gross-Neveu model with chiral imbalance
• Spatially oscillating correlation functions in $\left(2+1\right)$-dimensional four-fermion models: The mixing of scalar and vector modes at finite density
• Dense Quark-Gluon Plasma in strong magnetic fields
• Quantum criticality of magnetic catalysis in two-dimensional correlated Dirac fermions
• Anatomy of the magnetic catalysis by renormalization-group method
• Anomalous enhancement of Neel order in the $S=1/2$ square lattice Heisenberg model under fictitious magnetic field
• Fate of chiral symmetry in Riemann-Cartan geometry