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A self-consistent second-order Green's-function theory of a one-dimensional Heisenberg antiferromagnet, exhibiting spin waves without long-range order, is shown to yield qualitatively different results than a hybrid version treated by Richards. Comparison with exact and computer solutions for energy shows that the self-consistent solution represents a substantial improvement in local spin behavior at low temperatures. Long-range spin behavior at low temperatures is not correctly predicted by the self-consistent theory.
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Scales et al. (1972) studied this question.
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