  We study the extended Hubbard model on a two-dimensional half-filled square
lattice using the dynamical cluster approximation. We present results on the
phase boundaries between the paramagnetic metallic (normal) state and the
insulating antiferromagnetic state, as well as between the antiferromagnetic
and charge order states. We find hysteresis along the antiferromagnet/charge
order and normal/charge order phase boundaries (at larger values of the on-site
interaction), indicating first order phase transitions. We show that nearest
neighbor interactions lower the critical temperature for the antiferromagnetic
phase. We also present results for the effect of nearest neighbor interactions
on the antiferromagnetic phase boundary and for the evolution of spectral
functions and energetics across the phase transitions.
