  We propose a novel approach to the Graphene system using a local field theory
of 4 dimensional QED model coupled to 2+1 dimensional Dirac fermions, whose
velocity is much smaller than the speed of light. Performing hybrid Monte Carlo
simulations of this model on the lattice, we compute the chiral condensate and
its susceptibility with different coupling constant, velocity parameter and
flavor number. We find that the chiral symmetry is dynamically broken in the
small velocity regime and obtain a qualitatively consistent behavior with the
prediction from Schwinger-Dyson equations.
