Critical flavor number in the three dimensional Thirring model

Abstract

We present results of a Monte Carlo simulation of the three dimensional Thirring model with the number of fermion flavors ${N}_{f}$ varied between 2 and 18. By identifying the lattice coupling at which the chiral condensate peaks, simulations are performed at couplings ${g}^{2}({N}_{f})$ corresponding to the strong coupling limit of the continuum theory. The chiral symmetry restoring phase transition is studied as ${N}_{f}$ is increased, and the critical number of flavors estimated as ${N}_{fc}=6.6(1)$. The critical exponents measured at the transition do not agree with self-consistent solutions of the Schwinger-Dyson equations; in particular, there is no evidence for the transition being of infinite order. Implications for the critical flavor number in ${\mathrm{QED}}_{3}$ are briefly discussed.