Journal article

Publication year: 2017

Journal: Physical Review D

Volume number: 96

Issue number: 9

ISSN: 2470-0010

eISSN: 2470-0029

Open access status: Green

DOI Link: https://doi.org/10.1103/PhysRevD.96.094504

Publisher: American Physical Society

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 flavor number N -> 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 renormalization 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 flavors, but no symmetry breaking for large N. But there is no consensus on the critical flavor number N-cr above which there is no phase transition anymore and on further details of the critical behavior. 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 behavior for even and odd flavor numbers is very different: for even flavor numbers, chiral and parity symmetry are always unbroken; for odd flavor numbers, parity symmetry is spontaneously broken below the critical flavor number N-ir(cr) = 9, while chiral symmetry is still unbroken.

Harvard Citation style: Wellegehausen, B., Schmidt, D. and Wipf, A. (2017) Critical flavor number of the Thirring model in three dimensions, Physical Review D, 96(9), Article 094504. https://doi.org/10.1103/PhysRevD.96.094504

APA Citation style: Wellegehausen, B., Schmidt, D., & Wipf, A. (2017). Critical flavor number of the Thirring model in three dimensions. Physical Review D. 96(9), Article 094504. https://doi.org/10.1103/PhysRevD.96.094504