Abstract
What is the zero-temperature ordering pattern of a Heisenberg anti-ferromagnet with large spin length S (and possibly small dilution), on the Kagome lattice, or others built from corner-sharing triangles and tetrahedra? First, I summarize the uses of effective Hamiltonians to resolve the large ground-state degeneracy, leading to long-range order of the usual kind. Secondly, I discuss the effects of dilution, in particular that the classical ground states become nonfrustrated, in that every simplex of spins is optimally satisfied. Of three explanations for this, the most satisfactory is the MoessnerChalker constraint enumeration. Quantum zero-point energy may compete with classical exchange energy in a diluted system, creating frustration and enabling a spin-glass state. I suggest that the regime of over 97% occupation is qualitatively different from the more strongly diluted regime. PACS Nos.: 75.10N, 75.50Ee, 75.40, 75.25+z
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