  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.
