Abstract
In the present paper, we investigate the existence of the antiferromagnetic long-range order in a $S=1$ spatially anisotropic antiferromagnetic Heisenberg model with a single-ion energy term. By applying the reflection-positivity method developed by Dyson, Lieb, and Simon [J. Stat. Phys. 53, 1019 (1988)], we are able to determine the parameter regions where either the longitudinal or the transverse antiferromagnetic long-range order exist. We find that the single-ion energy anisotropy has a strong influence on the critical value of the spin coupling constant between the one-dimensional integer-spin chains. Qualitatively, our results agree with the previous ones obtained by the mean-field theory and hence, reestablish the conclusions on a mathematically rigorous basis.
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