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