  We study the interplay of topological band structure and conventional
magnetic long-range order in spinful Haldane model with onsite repulsive
interaction. Using the dynamical cluster approximation with clusters of up to
24 sites we find evidence of a first order phase transition from a Chern
insulator at weak coupling to a topologically trivial antiferromagnetic
insulator at strong coupling. These results call into question a previously
found intermediate state with coexisting topological character and
antiferromagnetic long-range order. Experimentally measurable signatures of the
first order transition include hysteretic behavior of the double occupancy,
single-particle excitation gap and nearest neighbor spin-spin correlations.
This first order transition is contrasted with a continuous phase transition
from the conventional band insulator to the antiferromagnetic insulator in the
ionic Hubbard model on the honeycomb lattice.
