Numerical simulation of graphene in a magnetic field within the effective field theory

Monte Carlo simulation of graphene in an external magnetic field perpendicular to the plane of graphene has been reported. The calculations have been performed using the effective quantum field theory with a noncompact $(3 + 1)$-dimensional Abelian gauge field and $(2 + 1)$-dimensional Kogut–Susskind fermions. It has been revealed that the external magnetic field shifts the semimetal-insulator phase transition point toward higher dielectric constants of the substrate. The phase diagram of the semimetal-insulator phase transition has been plotted in the (dielectric constant of the substrate-magnetic field) plane.