Critical Behaviour in the Single Flavor Thirring Model in 2+1d

Abstract

Results of a lattice field theory simulation of the single-flavor Thirring model in 2+1 spacetime dimensions are presented. The lattice model is formulated using domain wall fermions as a means to recover the correct U(2) symmetries of the continuum model in the limit where wall separation $L_s\to \infty$. Simulations on $12^3,16^3\times L_s$, varying self-interaction strength $g^2$ and bare mass $m$ are performed with $L_s=8,\dots 48$, and the results for the bilinear condensate $⟨\bar{\psi }\psi ⟩$ fitted to a model equation of state assuming a U(2)$\to$U(1)$\otimes$U(1) symmetry-breaking phase transition at a critical $g_c^2$. First estimates for $g^{-2}a$ and critical exponents are presented, showing small but significant departures from mean-field values. The results confirm that a symmetry-breaking transition does exist and therefore the critical number of flavors for the Thirring model $N_c>1$. Results for both condensate and associated susceptibility are also obtained in the broken phase on $16^3\times 48$, suggesting that here the $L_s\to \infty$ extrapolation is not yet under control. We also present results obtained with the associated 2+1$d$ truncated overlap operator DOL demonstrating exponential localisation, a necessary condition for the recovery of U(2) global symmetry, but that recovery of the Ginsparg-Wilson condition as $L_s\to \infty$ is extremely slow in the broken phase.

25 pages, 16 figures, a reference added and 2 figure captions amended

References in corpus (5)

• UV fixed-point structure of the three-dimensional Thirring model
• Critical behavior of the (2+1)-dimensional Thirring model
• Critical Flavor Number in the Three Dimensional Thirring Model
• Critical flavour number of the Thirring model in three dimensions
• Towards Critical Physics in 2+1d with U(2N)-Invariant Fermions

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• Large-$N$ Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect
• Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model
• Conformality and self-duality of $N_f=2$ QED${}_3$
• Symmetries of Thirring models on 3d lattices
• The Planar Thirring Model with Kähler-Dirac Fermions
• Spectroscopy in the 2+1$d$ Thirring Model with $N=1$ Domain Wall Fermions
• Transition in the spectral gap of the massless overlap Dirac operator coupled to abelian fields in three dimensions
• Critical Behaviour in the Single Flavor Thirring Model in 2+1$d$ with Wilson Kernel Domain Wall Fermions
• Evaluation of the Bilinear Condensate of the Planar Thirring Model in the Strongly Coupled Region
• Higher-Dimensional Chirally Stabilized Fixed Points and Their Deformations
• Lattice Field Theory Analysis of the Chiral Heisenberg Model