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 f c = 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 QED3 are briefly discussed.PACS numbers: PACS: 11.10. Kk, 11.30.Rd, 11.15.Ha The study of quantum field theories in which the ground state shows a sensitivity to the number of fermion flavors N f is intrinsically interesting. According to certain approximate solutions of Schwinger-Dyson equations (SDEs), in d = 3 spacetime dimensions both quantum electrodynamics (QED 3 ) and the Thirring model display this phenomenon. Both models have been proposed as effective theories describing different regions of the cuprate phase diagram, Thirring describing the superconducting phase, while QED 3 supposedly describes the nonsuperconducting "pseudogap" behaviour seen in the underdoped regime [1,2]. The Thirring model is a theory of fermions interacting via a current contact interaction:where ψ i ,ψ i are four-component spinors, m is a parityconserving bare mass, and the index i runs over N f distinct fermion flavors. In the chiral limit m → 0 the Lagrangian (1) shares the same global U(1) chiral symmetry ψ → e iαγ5 ψ,ψ →ψe iαγ5 as QED 3 . Since the coupling g 2 has mass dimension −1, naive power-counting suggests that the model is non-renormalisable. However [3,4,5], an expansion in powers of 1/N f , rather than g 2

We present results from numerical simulations of three different 3d four-fermion models that exhibit Z 2 , U(1), and SU(2) × SU(2) chiral symmetries, respectively. We performed the simulations by using the hybrid Monte Carlo algorithm. We employed finite size scaling methods on lattices ranging from 8 3 to 40 3 to study the properties of the second order chiral phase transition in each model. The corresponding critical coupling defines an ultraviolet fixed point of the renormalization group. In our high precision simulations, we detected next-to-leading order corrections for various critical exponents and we found them to be in good agreement with existing analytical large-N f calculations.

We present results from numerical simulations of the Nambu−Jona-Lasinio model with an SU(2) ⊗ SU(2) chiral symmetry and N c = 4, 8, and 16 quark colors at nonzero temperature. We performed the simulations by utilizing the hybrid Monte Carlo and hybrid Molecular Dynamics algorithms. We show that the model undergoes a second order phase transition. The critical exponents measured are consistent with the classical 3d O(4) universality class and hence in accordance with the dimensional reduction scenario. We also show that the Ginzburg region is suppressed by a factor of 1/N c in accordance with previous analytical predictions.