Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model

Abstract

We study the Gross-Neveu model in $2+1$ dimensions in an external magnetic field $B$. We first summarize known mean-field results, obtained in the limit of large flavor number $N_{\mathrm{f}}$, before presenting lattice results using the overlap discretization to study one reducible fermion flavor, $N_{\mathrm{f}}=1$. Our findings indicate that the magnetic catalysis phenomenon, i.e., an increase of the chiral condensate with the magnetic field, persists beyond the mean-field limit for temperatures below the chiral phase transition and that the critical temperature grows with increasing magnetic field. This is in contrast to the situation in QCD, where the broken phase shrinks with increasing $B$ while the condensate exhibits a non-monotonic $B$-dependence close to the chiral crossover, and we comment on this discrepancy. We do not find any trace of inhomogeneous phases induced by the magnetic field.

arXiv comment10 pages + 4 pages appendix, 10 figures; some clarifications, corrected typos, added references

References in corpus (80)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• The NumPy array: a structure for efficient numerical computation
• The effects of topological charge change in heavy ion collisions: "Event by event P and CP violation"
• Exactly massless quarks on the lattice
• Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
• Physics of Strongly Magnetized Neutron Stars
• The QCD phase diagram for external magnetic fields
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• QCD quark condensate in external magnetic fields
• Dimensional Reduction and Catalysis of Dynamical Symmetry Breaking by a Magnetic Field
• "Strongly interacting matter in magnetic fields": an overview
• Chiral Determinant as an Overlap of Two Vacua
• Chiral Fermions on the Lattice
• Inverse magnetic catalysis and the Polyakov loop
• QCD Phase Transition in a Strong Magnetic Background
• Chiral Symmetry Restoration and $Z_N$ Symmetry
• Dynamical Flavor Symmetry Breaking by a Magnetic Field in $2+1$ Dimensions
• The Importance of Asymptotic Freedom for the Pseudocritical Temperature in Magnetized Quark Matter
• Magnetic catalysis and anisotropic confinement in QCD
• Inverse magnetic catalysis in the (2+1)-flavor Nambu--Jona-Lasinio and Polyakov--Nambu--Jona-Lasinio models
• Magnetic Fields Produced by Phase Transition Bubbles in the Electroweak Phase Transition
• Chiral Properties of Strong Interactions in a Magnetic Background
• Four - Fermi Theories in Fewer Than Four Dimensions
• On Primordial Magnetic Fields of Electroweak Origin
• Numerical Methods for the QCD Overlap Operator: I. Sign-Function and Error Bounds
• From relativistic quantum fields to condensed matter and back again: Updating the Gross-Neveu phase diagram
• Approaches to the sign problem in lattice field theory
• Inverse magnetic catalysis in the linear sigma model with quarks
• Chiral density waves in quark matter within the Nambu--Jona-Lasinio model in an external magnetic field
• Catalysis of Dynamical Flavor Symmetry Breaking by a Magnetic Field in $2+1$ Dimensions
• Deconfinement transition in two-flavour lattice QCD with dynamical overlap fermions in an external magnetic field
• QCD phase diagram in a magnetic background for different values of the pion mass
• Ginsparg-Wilson Relation and Ultralocality
• Coulomb interaction at the metal-insulator critical point in graphene
• Analytic results for the effective action
• Chiral Magnetic Spiral
• UV fixed-point structure of the three-dimensional Thirring model
• Phase transition induced by a magnetic field
• Magnetic Fields from Phase Transitions
• The magnetized effective QCD phase diagram
• Overlap in odd dimensions
• Inhomogeneous phases in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• The Four-Fermi Model in Three Dimensions at Non-Zero Density and Temperature
• Lattice QCD with Ginsparg-Wilson fermions
• Magnetized baryons and the QCD phase diagram: NJL model meets the lattice
• Novel Lifshitz point for chiral transition in the magnetic field
• Renormalization group flow of quartic perturbations in graphene: Strong coupling and large-N limits
• Chiral symmetry restoration in the three-dimensional four-fermion model at non-zero temperature and density
• Renormalization Group Study of Magnetic Catalysis in the 3d Gross-Neveu Model
• Inhomogeneous chiral symmetry breaking in dense neutron-star matter
• Inverse magnetic catalysis -- how much do we know about?
• QCD phase diagram in a magnetized medium from the chiral symmetry perspective: The linear sigma model with quarks and the Nambu--Jona-Lasinio model effective descriptions
• Thermal Conductivity in 3D NJL Model Under External Magnetic Field
• Regulator dependence of inhomogeneous phases in the 2+1-dimensional Gross-Neveu model
• Magnetic catalysis of parity breaking in a massive Gross-Neveu model and high-temperature superconductivity
• Parity breaking and phase transition induced by a magnetic field in high $T_c$ superconductors
• Inhomogeneous phases in one-dimensional mass- and spin-imbalanced Fermi gases
• Critical flavour number of the Thirring model in three dimensions
• Duality between quark-quark and quark-antiquark pairing in 1+1 dimensional large N models
• On the Critical Flavor Number in the 2+1$d$ Thirring Model
• Phase transitions in hexagonal, graphene-like lattice sheets and nanotubes under the influence of external conditions
• Baryons in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• From the Dirac Operator to Wess-Zumino Models on Spatial Lattices
• Phase diagram of the magnetized planar Gross-Neveu model beyond the large-N approximation
• Inhomogeneities in the $2$-Flavor Chiral Gross-Neveu Model
• Extracting the magnitude of magnetic field at freeze-out in heavy-ion collisions
• Critical Behaviour in the Single Flavor Thirring Model in 2+1d
• Absence of chiral symmetry breaking in Thirring models in 1+2 dimensions
• Inhomogeneous phases in the chirally imbalanced $2+1$-dimensional Gross-Neveu model and their absence in the continuum limit
• Ginsparg-Wilson Fermions in Odd Dimensions
• Dressed Wilson loops as dual condensates in response to magnetic and electric fields
• Wave Functions of the Proton Ground State in the Presence of a Uniform Background Magnetic Field in Lattice QCD
• Stability of homogeneous chiral phases against inhomogeneous perturbations in 2+1 dimensions
• Thermodynamics of a generalized graphene-motivated (2+1)-dimensional Gross-Neveu model beyond mean field within the Beth-Uhlenbeck approach
• Fermion-scalar interactions with domain wall fermions
• Ginsparg-Wilson Relation and Lattice Chiral Symmetry in Fermionic Interacting Theories
• An Effective Field Theory Model for One-Dimensional $\mathrm{CH}$ Chains: Effects at Finite Chemical Potential, Temperature and External Zeeman Magnetic Field
• Gross-Neveu model with overlap fermions
• Testing Fermion Universality at a Conformal Fixed Point
• Finite Temperature Schwinger Model

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