  Using a combination of quantum Monte Carlo simulations, functional
renormalization group calculations and mean-field theory, we study the Hubbard
model on the Bernal-stacked honeycomb bilayer at half-filling as a model system
for bilayer graphene. The free bands consisting of two Fermi points with
quadratic dispersions lead to a finite density of states at the Fermi level,
which triggers an antiferromagnetic instability that spontaneously breaks
sublattice and spin rotational symmetry once local Coulomb repulsions are
introduced. Our results reveal an inhomogeneous participation of the spin
moments in the ordered ground state, with enhanced moments at the three-fold
coordinated sites. Furthermore, we find the antiferromagnetic ground state to
be robust with respect to enhanced interlayer couplings and extended Coulomb
interactions.
