  We report on Hybrid-Monte-Carlo simulations of the tight-binding model with
long-range Coulomb interactions for the electronic properties of graphene. We
investigate the spontaneous breaking of sublattice symmetry corresponding to a
transition from the semimetal to an antiferromagnetic insulating phase. Our
short-range interactions thereby include the partial screening due to electrons
in higher energy states from ab initio calculations based on the constrained
random phase approximation [T.O.Wehling {\it et al.}, Phys.Rev.Lett.{\bf 106},
236805 (2011)]. In contrast to a similar previous Monte-Carlo study
[M.V.Ulybyshev {\it et al.}, Phys.Rev.Lett.{\bf 111}, 056801 (2013)] we also
include a phenomenological model which describes the transition to the
unscreened bare Coulomb interactions of graphene at half filling in the
long-wavelength limit. Our results show, however, that the critical coupling
for the antiferromagnetic Mott transition is largely insensitive to the
strength of these long-range Coulomb tails. They hence confirm the prediction
that suspended graphene remains in the semimetal phase when a realistic static
screening of the Coulomb interactions is included.
