Is Graphene in Vacuum an Insulator?

We present evidence, from lattice Monte Carlo simulations of the phase diagram of graphene as a function of the Coulomb coupling between quasiparticles, that graphene in vacuum is likely to be an insulator. We find a semimetal-insulator transition at alpha(crit)(g)=1.11 +/- 0.06, where alpha(g)similar or equal to 2.16 in vacuum, and alpha(g)similar or equal to 0.79 on a SiO2 substrate. Our analysis uses the logarithmic derivative of the order parameter, supplemented by an equation of state. The insulating phase disappears above a critical number of four-component fermion flavors 4 < N-f(crit)< 6. Our data are consistent with a second-order transition.