For the Haldane-Shastry spin chain, the nonlocal factor caused by ring frustration is exactly cos(pi*alpha) with alpha = r/N, matching the Heisenberg model.
Baker, etc, Proc
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Nonlocal behaviors of spin correlations in the Haldane-Shastry model
For the Haldane-Shastry spin chain, the nonlocal factor caused by ring frustration is exactly cos(pi*alpha) with alpha = r/N, matching the Heisenberg model.