Critical behavior in the single flavor Thirring model in 2+1D

Hands, Simon ORCID: 0000-0001-5720-7852, Mesiti, Michele and Worthy, Jude (2020) Critical behavior in the single flavor Thirring model in 2+1D. PHYSICAL REVIEW D, 102 (9). 094502-.

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Official URL: http://dx.doi.org/10.1103/PhysRevD.102.094502

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 $L_s = 8, \ldots 48$, and the results for the bilinear condensate $\langle\bar\psi\psi\rangle$ 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 $16^3\times48$, 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.

Item Type:	Article
Additional Information:	25 pages, 16 figures, a reference added and 2 figure captions amended
Uncontrolled Keywords:	hep-lat, hep-lat, hep-th
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	06 Mar 2023 09:28
Last Modified:	06 Mar 2023 09:28
DOI:	10.1103/PhysRevD.102.094502
Open Access URL:	https://journals.aps.org/prd/abstract/10.1103/Phys...
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3168761