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The kagome lattice is based on corner-sharing triangles, rather than tetrahedra. Whereas four spins on a single tetrahedron have an internal ground-state degeneracy, three spins on a triangle do not; however, an extensive degeneracy arises as the ground-state constraints of different triangles can cease to be independent, as happens for coplanar states.
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O. Tchernyshyov et al., work in progress
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O. Tchernyshyov et al., work in progress.
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39
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4344579254
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note
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Also, these authors point out that several of the smaller systems display symmetries on top of the ones present for the infinite lattice.
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For an introduction to height representation theory close to the perspective of this paper, see C. Zeng and C. L. Henley, Phys. Rev. B 55:14935 (1997).
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The derivation is given in S. Lukyanov and V. Terras, hep-th/0206093
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Lukyanov, S.1
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46
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4344710848
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note
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The correlations in this phase are governed by the Gaussian combination of Eqs. (8.5) and (8.6). These lead to a factorized height correlator whose in plane form is different from that for an uncoupled plane only by an overall normalization. That in turn, is small at small interlayer coupling.
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