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. It is shown that for all considered temperatures the interaction can be well described by the Debye screened potential created by two-dimensional electron-hole excitations. At low temperatures Debye mass $m_D$ plays a role of order parameter of the insulator-semimetal phase transition. In the semimetal phase at high temperature graphene reveals the properties of weakly interacting two-dimensional plasma of fermions excitations.