  The Thirring model is a four fermion theory with vector interaction. We study
it in three dimensions, where it is closely related to QED and other models
used to describe properties of graphene. In addition it is a good toy model to
study chiral symmetry breaking, since a phase with broken chiral symmetry is
present for the model with one fermion flavour. On the other hand, there is no
such phase in the limit of infinitely many fermion flavours. Thus, a transition
at some critical flavour number Nfc is expected, where the broken phase
vanishes. The model was already studied with different methods, including
Schwinger-Dyson, functional renormalization group and lattice approaches. Most
studies agree that there is indeed a phase transition from a chirally symmetric
phase to a spontaneously broken phase for a small number of fermion flavours.
But there is no agreement on the critical flavour number and further details of
the critical behaviour. Values of Nfc found in the literature usually range
between 2 and 7. All earlier lattice studies were performed with staggered
fermions, where it is questionable if the continuum limit of the lattice model
has the same chiral symmetry as the continuum model. We present an approach for
simulations of the Thirring model with SLAC fermions. With this choice, we can
be sure to implement the full chiral symmetry of the continuum model. First
results from simulations are shown but do not allow a reliable estimate of Nfc
so far.
