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We have treated the 1-D Heisenberg antiferromagnet in a mean-field theory, and determined a phase diagram showing the regions for the antiferromagnetic state, the spin-Peierls state and the paramagnetic state. When a spin-phonon coupling constant is greater than 1.08, the antiferromagnetic state is stable below a Néel temperature T N =0.568 J / k B . When it is less than 1.08, the spin-Peierls state is stable below a transition temperature T P , which is higher than T N and increases as the coupling constant decreases.
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Kondo et al. (1982) studied this question.
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