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.

11 pages, 5 figures, 1 ancillary Mathematica notebook

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Cited by in corpus (22)

• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Four loop renormalization of the Gross-Neveu model
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• Shocks and quark-meson scatterings at large density
• Impact of generalized Yukawa interactions on the lower Higgs mass bound
• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Momentum dependence of quantum critical Dirac systems
• Fermionic multicriticality near Kekulé valence-bond ordering in honeycomb lattice
• On the Question of a Possible Infrared Zero in the Beta Function of the Finite-$N$ Gross-Neveu Model
• Twisted bilayer graphene at charge neutrality: competing orders of SU(4) Dirac fermions
• Angle-Tuned Gross-Neveu Quantum Criticality in Twisted Bilayer Graphene: A Quantum Monte Carlo Study
• 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
• Scale symmetry breaking and generation of mass at quantum critical points
• Quantum field theories of relativistic Luttinger fermions
• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• Continued functions and critical exponents: Tools for analytical continuation of divergent expressions in phase transition studies
• Strong-coupling superconductivity near Gross-Neveu quantum criticality in Dirac systems
• Renormalization Flow of Nonlinear Electrodynamics
• Boundary critical behavior of the Gross-Neveu-Yukawa model
• Mean-field theory for self-interacting relativistic Luttinger fermions