A study of a simple band model of a commensurate, two-dimensional anti
ferromagnet is briefly described. A self-consistent calculation shows
a transition from a paramagnetic to a metallic antiferromagnetic state
when an interaction is stronger than a critical value. The transition
is accompanied by a change in size (large to small) of the Fermi surf
ace. An insulating state may be obtained if there is exactly one elect
ron per site.