Interaction of static charges in graphene within Monte-Carlo simulation

The study of the interaction potential between static charges within Monte-Carlo simulation of graphene is carried out. The numerical simulations are performed in the effective lattice field theory with noncompact 3 + 1-dimensional Abelian lattice gauge fields and 2 + 1-dimensional staggered lattice fermions. At low temperature the interaction can be described by the Coulomb potential reduced by some dielectric permittivity eR. The dependence of the eR on the dielectric permittivity of substrate is determined. In addition, the renormalization of the quasiparticle charge is studied. At large temperatures the interaction potential can be described by the two dimensional Debye screening. The dependence of Debye screening mass on the dielectric permittivity of substrate allows to determine the position of the insulator-semimetal phase transition. It is shown that graphene reveals in the semimetal phase the properties of the two-dimensional plasma of fermions excitations.