We investigate spectral functions extracted using the maximum entropy method from correlators measured in lattice simulations of the (2ϩ1)-dimensional four-fermion model. This model is particularly interesting because it has both a chirally broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are only resonances. In the broken phase we study the elementary fermion, pion, sigma, and massive pseudoscalar meson; our results confirm the Goldstone nature of the and permit an estimate of the meson binding energy. We have, however, seen no signal of → decay as the chiral limit is approached. In the symmetric phase we observe a resonance of nonzero width in qualitative agreement with analytic expectations; in addition the ultraviolet behavior of the spectral functions is consistent with the large nonperturbative anomalous dimension for fermion composite operators expected in this model.

No abstract

A 2+1 dimensional fermion field theory is proposed as a model for the lowenergy electronic excitations in monolayer graphene. The model consists of N f = 2 fourcomponent Dirac fermions moving in the plane and interacting via a contact interaction between charge densities. For strong couplings there is a continuous transition to a Mott insulting phase. We present results of an extensive numerical study of the model's critical region, including the order parameter, its associated susceptibility, and for the first time the quasiparticle propagator. The data enables an extraction of the critical exponents at the transition, including the dynamical critical exponent, which are hypothesised to be universal features of a quantum critical point. The relation of our model with others in the literature is discussed, along with the implications for physical graphene following from our value of the critical coupling.

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