Ising and Gross-Neveu model in next-to-leading order

Abstract

We study scalar and chiral fermionic models in next-to-leading order with the help of the functional renormalisation group. Their critical behaviour is of special interest in condensed matter systems, in particular graphene. To derive the beta functions, we make extensive use of computer algebra. The resulting flow equations were solved with pseudo-spectral methods to guarantee high accuracy. New estimates on critical quantities for both the Ising and the Gross-Neveu model are provided. For the Ising model, the estimates agree with earlier renormalisation group studies of the same level of approximation. By contrast, the approximation for the Gross-Neveu model retains many more operators than all earlier studies. For two Dirac fermions, the results agree with both lattice and large-$N_f$ calculations, but for a single flavour, different methods disagree quantitatively, and further studies are necessary.

arXiv comment11 pages, 5 figures, 1 ancillary Mathematica notebook

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Cited by in corpus (49)

• The nonperturbative functional renormalization group and its applications
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Bootstrapping 3D Fermions with Global Symmetries
• Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems
• Status of the asymptotic safety paradigm for quantum gravity and matter
• Critical behavior of Dirac fermions from perturbative renormalization
• Four loop renormalization of the Gross-Neveu model
• Constraining power of asymptotic safety for scalar fields
• Lorentz invariance violations in the interplay of quantum gravity with matter
• Fractionalized fermionic quantum criticality in spin-orbital Mott insulators
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• Fermion-induced quantum criticality with two length scales in Dirac systems
• Infinite order quantum-gravitational correlations
• Exact RG Flow Equations and Quantum Gravity
• Shocks and quark-meson scatterings at large density
• Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality
• Impact of generalized Yukawa interactions on the lower Higgs mass bound
• Predictive power of grand unification from quantum gravity
• Compatible orders and fermion-induced emergent symmetry in Dirac systems
• Confinement transition in the QED${}_3$-Gross-Neveu-XY universality class
• A functional perspective on emergent supersymmetry
• Itinerant quantum multi-criticality of two dimensional Dirac fermions
• Fractionalized quantum criticality in spin-orbital liquids from field theory beyond the leading order
• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Momentum dependence of quantum critical Dirac systems
• Chiral tricritical point: a new universality class in Dirac systems
• Fermionic multicriticality near Kekulé valence-bond ordering in honeycomb lattice
• Torus Spectroscopy of the Gross-Neveu-Yukawa Quantum Field Theory: Free Dirac versus Chiral Ising Fixed Point
• Emergent symmetries and coexisting orders in Dirac fermion systems
• On the Question of a Possible Infrared Zero in the Beta Function of the Finite-$N$ Gross-Neveu Model
• Asymptotic freedom in $Z_2$-Yukawa-QCD models
• Trion states and quantum criticality of attractive SU(3) Dirac fermions
• Angle-Tuned Gross-Neveu Quantum Criticality in Twisted Bilayer Graphene: A Quantum Monte Carlo Study
• Exact solutions and residual regulator dependence in functional renormalisation group flows
• Twisted bilayer graphene at charge neutrality: competing orders of SU(4) Dirac fermions
• Bond-ordered states and $f$-wave pairing of spinless fermions on the honeycomb lattice
• Relativistic Mott transitions and finite-temperature effects of quantum criticality in Dirac semimetals
• Absence of SO(4) quantum criticality in Dirac semimetals at two-loop order
• SO(4) multicriticality of two-dimensional Dirac fermions
• Spin Stiffness and Domain Walls in Dirac-Electron Mediated Magnets
• Scale symmetry breaking and generation of mass at quantum critical points
• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• Quantum field theories of relativistic Luttinger fermions
• Strong-coupling superconductivity near Gross-Neveu quantum criticality in Dirac systems
• Continued functions and critical exponents: Tools for analytical continuation of divergent expressions in phase transition studies
• Renormalization Flow of Nonlinear Electrodynamics
• Mean-field theory for self-interacting relativistic Luttinger fermions
• Boundary critical behavior of the Gross-Neveu-Yukawa model