  A model for a Heisenberg antiferromagnet on a pyrochlore lattice with
exchange and dipole-dipole interactions is studied via mean-field theory. In
treating the dipoles by use of the Ewald method, a soft (critical) mode with a
unique ordering wave vector is selected for all strengths of the dipole-dipole
coupling. For weak dipoles a partially ordered, three sublattice spin structure
(P state), with q_{ord}= (1/2 1/2 1/2), is selected. A fully ordered, four
sublattice spin structure (F state), with q = (000), competes with the P state
and becomes the stable structure as the temperature is reduced. Our results are
compared against other theoretical calculations and connections to recent
experimental results for Gd2Ti2O7 are discussed.
