Critical flavour number of the Thirring model in three dimensions

Abstract

The Thirring model is a four-fermion theory with a current-current interaction and $U(2N)$ chiral symmetry. It is closely related to three-dimensional QED and other models used to describe properties of graphene. In addition it serves as a toy model to study chiral symmetry breaking. In the limit of flavour number $N\to 1/2$ it is equivalent to the Gross-Neveu model, which shows a parity-breaking discrete phase transition. The model was already studied with different methods, including Dyson-Schwinger equations, functional renormalisation group methods and lattice simulations. Most studies agree that there is a phase transition from a symmetric phase to a spontaneously broken phase for a small number of fermion flavours, but no symmetry breaking for large $N$. But there is no consensus on the critical flavour number $N^{\text{cr}}$ above which there is no phase transition anymore and on further details of the critical behaviour. Values of $N$ found in the literature vary between $2$ and $7$. All earlier lattice studies were performed with staggered fermions. Thus it is questionable if in the continuum limit the lattice model recovers the internal symmetries of the continuum model. We present new results from lattice Monte Carlo simulations of the Thirring model with SLAC fermions which exactly implement all internal symmetries of the continuum model even at finite lattice spacing. If we reformulate the model in an irreducible representation of the Clifford algebra, we find, in contradiction to earlier results, that the behaviour for even and odd flavour numbers is very different: For even flavour numbers, chiral and parity symmetry are always unbroken. For odd flavour numbers parity symmetry is spontaneously broken below the critical flavour number $N_{\text{ir}}^{\text{cr}}=9$ while chiral symmetry is still unbroken.

17 pages, 9 figures, 3 tables

References in corpus (10)

• Quantum Critical Behaviour in a Graphene-like Model
• UV fixed-point structure of the three-dimensional Thirring model
• Critical behavior of the (2+1)-dimensional Thirring model
• Low-dimensional Supersymmetric Lattice Models
• Critical Flavor Number in the Three Dimensional Thirring Model
• Two-Dimensional Wess-Zumino Models at Intermediate Couplings
• Critical behaviour of reduced QED${}_{4,3}$ and dynamical fermion gap generation in graphene
• Abelian color cycles: a new approach to strong coupling expansion and dual representations for non-abelian lattice gauge theory
• Towards Critical Physics in 2+1d with U(2N)-Invariant Fermions
• A local fermion update algorithm for SYM quantum mechanics

Cited by in corpus (6)

• Momentum dependence of quantum critical Dirac systems
• Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model
• Symmetries of Thirring models on 3d lattices
• The Planar Thirring Model with Kähler-Dirac Fermions
• The relevance of the three dimensional Thirring coupling at finite temperature and density
• Hartree-Fock approach to dynamical mass generation in the generalized (2+1)-dimensional Thirring model