  We present Monte Carlo simulation results for the three dimensional Thirring
model for numbers of fermion flavors N_f=4 and 6. For N_f=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 N_f=2. For N_f=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 N_f are briefly discussed.
