Three-dimensional thirring model for small Nf Original Research Article

We formulate the three-dimensional Thirring model on a space-time lattice and study it for various even numbers of fermion flavours Nf by Monte Carlo simulation. We find clear evidence for spontaneous chiral symmetry breaking at strong coupling, contradicting the predictions of the 1Nf 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 Nf = 2 and Nf = 4, while no fit is found for Nf = 6, suggesting there is a critical number Nfc < 6 beyond which no chiral symmetry breaking occurs. The spectrum of the Nf = 2 theory is studied; the states examined vary sharply but continuously across the transition.