These complex antiferromagnets have nearly degenerate ground states, and it is challenging to figure out how small perturbations single out one of them as being the true ground state, or produce an exotic disordered state which is a superposition of many configurations. (Recent theses, Uzi Hizi '06; current undergrad, Sophia Sklan '10).
In the systems I study, the spins have length > 1/2. Thus the naive approach (as works in most magnetic systems) is to expand around the classical ground state -- but which ground state? since they are highly degenerate. Hence it's necessary to set up a perturbation theory to expand around an unspecified state. A common phenomenon in the business is "order by disorder": that means the degeneracy gets resolved (and long-range order develops) precisely due to the strong fluctuations associated with the degeneracy, or perhaps due to quenched randomness (e.g. substitution of the moments by nonmagnetic ions). Uzi Hizi (PhD '06) worked out how quantum fluctuations resolve the degeneracy of the spin-ordering pattern of pyrochlore antiferromagnets.
I've also studied 2D discrete models with "height" (interface) representations, which connects to the theory of exact solutions and to conformal field theory (past collaborators Dr. Jane Kondev and Dr. Chen Zeng.) Such models are currently used in toy models of highly frustrated and/or exotic kinds of order, in (a) quantum systems [See "From classical to quantum dynamics at Rokhsar-Kivelson points" , or (b) in three-dimensional systems Grad Zach Lamberty is currently simulating an outgrowth of such models using the elements of non-abelian groups as the "spin variables", in order to realize classical topological order.
(Sorry, incomplete). Lumped in with frustration, we are also interested in the states of quantum spins placed on a lattice in which many of the magnetic atoms are replaced randomly by non-magnetic ones, such that it is at the critical percolation threshold.