Critical Flavor Number in the Three Dimensional Thirring Model

TL;DR

This study uses Monte Carlo simulations to determine the critical number of fermion flavors in the three-dimensional Thirring model, finding N_{fc}≈6.6 and analyzing the nature of the phase transition.

Contribution

It provides the first Monte Carlo estimate of the critical flavor number in the 3D Thirring model and examines the phase transition characteristics.

Findings

Critical flavor number N_{fc} ≈ 6.6

Chiral phase transition is not of infinite order

Measured critical exponents differ from Schwinger-Dyson predictions

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 be 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 QED_3 are briefly discussed.