  We present the first results of numerical simulations of a 2+1 dimensional
fermion field theory based on a recent proposal for a model of graphene,
consisting of N_f four-component Dirac fermions moving in the plane and
interacting via an instantaneous Coulomb interaction. In the strong-coupling
limit we identify a critical number of flavors N_fc=4.8(2) separating an
insulating from a conducting phase. This transition corresponds to the location
of a quantum critical point, and we use a fit to the equation of state for the
chiral order parameter to estimate the critical exponents. Next we simulate
N_f=2 corresponding to real graphene, and approximately locate a transition
from strong to weak coupling behaviour. Strong correlations are evident in the
weak-coupling regime.
