Three-dimensional thirring model for small Nf

Abstract

We formulate the three-dimensional Thirring model on a space-time lattice and study it for various even numbers of fermion flavours N f by Monte Carlo simulation. We find clear evidence for spontaneous chiral symmetry breaking at strong coupling, contradicting the predictions of the 1 N f expansion. The critical point appears to correspond to an ultraviolet fixed point of the renormalisation group; a fit to a RG-inspired equation of state in the vicinity of the fixed point yields distinct critical exponents for N f = 2 and N f = 4, while no fit is found for N f = 6, suggesting there is a critical number N fc < 6 beyond which no chiral symmetry breaking occurs. The spectrum of the N f = 2 theory is studied; the states examined vary sharply but continuously across the transition.