  We present results for the equation of state of a graphene-like model in an
effort to understand the properties of its quantum phase transition. The N_f
fermion species interact through a three dimensional instantaneous Coulomb
potential. Since there are no reliable analytical tools that work for all
values of N_f and the coupling constant g, we rely on Monte Carlo simulations
to calculate the critical properties of the model near the phase transition. We
consider the four-component formulation for the fermion fields, which arises
naturally as the continuum limit of the staggered fermion construction in (2+1)
dimensions. In the limit of infinitely strong Coulomb interaction, the system
undergoes a quantum phase transition at a critical number of fermion species
N_fc ~ 4.7. We also calculate the values of the critical exponents at the
quantum phase transition.
