Depleted pyrochlore antiferromagnets

摘要: I consider the class of "depleted pyrochlore" lattices corner-sharing triangles, made by removing spins from a pyrochlore lattice such that every tetrahedron loses exactly one. Previously known examples are "hyperkagome" and "kagome staircase". give criteria in terms loops for whether given depleted can order analogous to kagome \sqrt{3} \times \sqrt{three} state, also show how pseudo-dipolar correlations (due local constraints) generalize even random case.