Article
Version 1
Preserved in Portico This version is not peer-reviewed
Symmetries of Thirring Models on 3D Lattices
Version 1
: Received: 1 January 2022 / Approved: 6 January 2022 / Online: 6 January 2022 (10:20:20 CET)
A peer-reviewed article of this Preprint also exists.
Wipf, A.W.; Lenz, J.J. Symmetries of Thirring Models on 3D Lattices. Symmetry 2022, 14, 333. Wipf, A.W.; Lenz, J.J. Symmetries of Thirring Models on 3D Lattices. Symmetry 2022, 14, 333.
Abstract
We review some recent developments about strongly interacting relativistic Fermi theories in three spacetime dimensions. These models realize the asymptotic safety scenario and are used to describe the low-energy properties of Dirac materials in condensed matter physics. We begin with a general discussion of the symmetries of multi-flavor Fermi systems in arbitrary dimensions. Then we review known results about the critical flavor number $N_\mathrm{crit}$ of Thirring models in three dimensions. Only models with flavor number below $N_\mathrm{crit}$ show a phase transition from a symmetry-broken strong-coupling phase to a symmetric weak-coupling phase. Recent simulations with chiral fermions show that $N_\mathrm{crit}$ is smaller than previously extracted with various non-perturbative methods. Our simulations with chiral SLAC fermions reveal that for four-component flavors $N_\mathrm{crit}=0.80(4)$. This means that all reducible Thirring models with $\Nr=1,2,3,\dots$ show no phase transition with order parameter. Instead we discover footprints of phase transitions without order parameter. These new transitions are probably smooth and could be used to relate the lattice Thirring models to Thirring models in the continuum. For a single irreducible flavor, we provide previously unpublished values for the critical couplings and critical exponents.
Keywords
Model field theory; chiral symmetry breakin; parity breaking; dynamical fermions; four-Fermi theories; Thirring models
Subject
Physical Sciences, Particle and Field Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment