  We investigate the consequences for geometrically frustrated antiferromagnets
of weak disorder in the strength of exchange interactions. Taking as a model
the classical Heisenberg antiferromagnet with nearest neighbour exchange on the
pyrochlore lattice, we examine low-temperature behaviour. We show that random
exchange generates long-range effective interactions within the extensively
degenerate ground states of the clean system. Using Monte Carlo simulations, we
find a spin glass transition at a temperature set by the disorder strength.
Disorder of this type, which is generated by random strains in the presence of
magnetoelastic coupling, may account for the spin freezing observed in many
geometrically frustrated magnets.
