Absence of chiral symmetry breaking in Thirring models in 1+2 dimensions

Understand

The Thirring model is an interacting fermion theory with current-current interaction.

• The model in $1+2$ dimensions has applications in condensed-matter physics to describe the electronic excitations of Dirac materials.
• Earlier investigations with Schwinger-Dyson equations, the functional renormalization group and lattice simulations with staggered fermions suggest that a critical number of (reducible) flavors $N^{\mathrm{c}}$ exists, below which chiral symmetry can be broken spontaneously.
• Values for $N^{\mathrm{c}}$ found in the literature vary between $2$ and $7$.