Abstract
We present the 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 behavior. Strong correlations are evident in the weak-coupling regime.
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