Certain lattice structures create conflicting interactions for
spins residing on such a lattice. At the classical level, spin
frustration translates into a large number of degenerate ground
states and to disruption of magnetic order even at low temperatures.
Quantum effects lift the classical degeneracy and may produce a ground
state with interesting properties. I will present the results of our
recent studies of the Heisenberg antiferromagnet on the pyrochlore
lattice and its two-dimensional analogs, where we find ground states
and thermal ensembles with valence-bond order.
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