The three-dimensional Thirring model for Nƒ = 4 and Nƒ = 6 Original Research Article

We present Monte Carlo simulation results for the three-dimensional Thirring model for numbers of fermion flavours Nƒ = 4 and 6. For Nf = 4 we find a second-order chiral symmetry breaking transition at strong coupling, corresponding to an ultra-violet fixed point of the renormalisation group defining a non-trivial continuum limit. The critical exponents extracted from a fit to a model equation of state are distinct from those found for Nƒ = 2. For Nƒ = 6, in contrast, we present evidence for tunnelling between chirally symmetric and broken vacua at strong coupling, implying that the phase transition is first-order and no continuum limit exists. The implications for the phase diagram of the model in the plane of coupling strength and Nƒ are briefly discussed.