UV fixed-point structure of the three-dimensional Thirring model

Abstract

We investigate the UV fixed-point structure of the three-dimensional Thirring model by means of the functional renormalization group (RG). We classify all possible 4-fermi interactions compatible with the present chiral and discrete symmetries and calculate the purely fermionic RG flow using a full basis of fermionic four-point functions in the point-like limit. Our results show that the UV complete (asymptotically safe) Thirring model lies in a two-dimensional coupling plane which reduces to the conventional Thirring coupling only in the strict large-Nf limit. In addition to the Thirring universality class which is characterized by one relevant direction (also at finite Nf), two further interacting fixed points occur which may define new universality classes of second-order phase transitions also involving parity-broken phases. The Nf-dependence of the Thirring fixed point sheds further light on the existence of an Nf-controlled quantum phase transition above which chiral symmetry remains unbroken for arbitrary large coupling, even though a definite answer will require a direct computation of competing orders.

11 pages, 5 figures, REVTeX

References in corpus (60)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Chiral tunneling and the Klein paradox in graphene
• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Aspects of the Functional Renormalisation Group
• Quantum-limited shot noise in graphene
• Optimised Renormalisation Group Flows
• Zitterbewegung, chirality, and minimal conductivity in graphene
• Interactions and phase transitions on graphene's honeycomb lattice
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Is graphene in vacuum an insulator?
• Theory of interacting electrons on the honeycomb lattice
• Lectures on the functional renormalization group method
• Conformal Phase Transition in Gauge Theories
• QED3 theory of pairing pseudogap in cuprates: From d-wave superconductor to antiferromagnet via "algebraic" Fermi liquid
• The Zero Temperature Chiral Phase Transition in SU(N) Gauge Theories
• Algebraic Fermi liquid from phase fluctuations: "topological" fermions, vortex "berryons" and QED3 theory of cuprate superconductors
• Renormalization Flow of Bound States
• QED3 theory of underdoped high temperature superconductors
• A New Constraint on Strongly Coupled Field Theories
• Chiral phase structure of QCD with many flavors
• Chiral phase boundary of QCD at finite temperature
• Supersymmetry Inspired QCD Beta Function
• The Influence of the Full Vertex and Vacuum Polarization on the Fermion Propagator in QED3
• Quantum Critical Behaviour in a Graphene-like Model
• Antiferromagnetism from phase disordering of a d-wave superconductor
• Dynamical Chiral Symmetry Breaking in Unquenched ${QED}_3$
• The Phase Structure of an SU(N) Gauge Theory with N_f Flavors
• Exact flow equation for composite operators
• The infrared dynamics of Minimal Walking Technicolor
• Renormalization group flows into phases with broken symmetry
• Monte Carlo Simulation of the Semimetal-Insulator Phase Transition in Monolayer Graphene
• Towards a renormalizable standard model without fundamental Higgs scalar
• Non-Compact QED_3 with N_f=1 and N_f=4
• Non-compact QED_3 with N_f >=2
• Running coupling at finite temperature and chiral symmetry restoration in QCD
• Phase structure of lattice QCD for general number of flavors
• Gauge invariance of a critical number of flavours in QED3
• Chiral symmetry breaking in ${\mathrm{QED}}_3$ in presence of irrelevant interactions: a renormalization group study
• Conformal Window of Gauge Theories with Four-Fermion Interactions and Ideal Walking
• Critical Flavor Number in the Three Dimensional Thirring Model
• Effective theory of high-temperature superconductors
• Dynamical Symmetry Breaking in QED_3 from the Wilson RG Point of View
• Scaling laws near the conformal window of many-flavor QCD
• Infrared cutoff dependence of the critical flavor number in three-dimensional QED
• Thirring Model as a Gauge Theory
• Meson masses in large Nf QCD from the Bethe-Salpeter equation
• Chiral Gap and Collective Excitations in Monolayer Graphene from Strong Coupling Expansion of Lattice Gauge Theory
• O(1/N_f) Corrections to the Thirring Model in 2<d<4
• Large-N analysis of (2+1)-dimensional Thirring model
• Thirring Model as a Gauge Theory
• The Phase Diagram of the Three Dimensional Thirring Model
• Phase transition and critical behavior of d=3 chiral fermion models with left/right asymmetry
• The Three Dimensional Thirring Model for N_f=4 and N_f=6
• The Conformal Window of deformed CFT's in the planar limit
• Fermion Mass Generation in the D-dimensional Thirring Model as a Gauge Theory
• Anomalous scaling of fermions and order parameter fluctuations at quantum criticality
• Dynamical chiral symmetry breaking in QED${}_3$ at finite density and impurity potential
• Do Three Dimensions tell us Anything about a Theory of Everything?

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• Gross-Neveu-Heisenberg criticality from competing nematic and antiferromagnetic orders in bilayer graphene
• Universal behavior of coupled order parameters below three dimensions
• Non-Abelian Chern-Simons Theory from a Hubbard-like Model
• Asymptotic safety on the lattice: The Nonlinear O(N) Sigma Model
• Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model
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