  We consider the effect of geometric frustration induced by the random
distribution of loop lengths in the "fat" graphs of the dynamical
triangulations model on coupled antiferromagnets. While the influence of such
connectivity disorder is rather mild for ferromagnets in that an ordered phase
persists and only the properties of the phase transition are substantially
changed in some cases, any finite-temperature transition is wiped out due to
frustration for some of the antiferromagnetic models. A wealth of different
phenomena is observed: while for the annealed average of quantum gravity some
graphs can adapt dynamically to allow the emergence of a Neel ordered phase,
this is not possible for the quenched average, where a zero-temperature
spin-glass phase appears instead. We relate the latter to the behaviour of
conventional spin-glass models coupled to random graphs.
