  We study geometrically frustrated antiferromagnets with magnetoelastic
coupling. Frustration in these systems may be relieved by a structural
transition to a low temperature phase with reduced lattice symmetry. We examine
the statistical mechanics of this transition and the effects on it of quenched
disorder, using Monte Carlo simulations of the classical Heisenberg model on
the pyrochlore lattice with coupling to uniform lattice distortions. The model
has a transition between a cubic, paramagnetic high-temperature phase and a
tetragonal, Neel ordered low-temperature phase. It does not support the
spin-Peierls phase, which is predicted as an additional possibility within
Landau theory, and the transition is first-order for reasons unconnected with
the symmetry analysis of Landau theory. Quenched disorder stabilises the cubic
phase, and we find a phase diagram as a function of temperature and disorder
strength similar to that observed in ZnCdCrO.
