  Many classical, geometrically frustrated antiferromagnets have
macroscopically degenerate ground states. In a class of three-dimensional
systems, the set of degenerate ground states has power-law correlations and is
an example of a Coulomb phase. We investigate Neel ordering from such a Coulomb
phase, induced by weak additional interactions that lift the degeneracy. We
show that the critical point belongs to a universality class that is different
from the one for the equivalent transition out of the paramagnetic phase, and
that it is characterised by effective long-range interactions; alternatively,
ordering may be discontinuous. We suggest that a transition of this type may be
realised by applying uniaxial stress to a pyrochlore antiferromagnet.
