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Solid State Communications

Frustrated three dimensional anisotropic antiferromagnet with single ion anisotropy

Antonio S. T. Pires

Published Jan 23, 2014• 3 citations
Publisher
DOI
10.1016/j.ssc.2014.01.015

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In the present paper, we investigate the existence of the antiferromagnetic long-range order in a S=1S=1S=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.
In the present paper, we investigate the quantum phase transition in a spatially anisotropic antiferromagnetic Heisenberg model of S = 1 with single-ion energy anisotropy. By using the Schwinger boson representation, we calculate the Gaussian correction to the critical value J ⊥ c caused by quantum spin fluctuations. We find that, for the positive single-ion energy, a nonzero value of J ⊥ c is always needed to stabilize the antiferromagnetic long-range order in this model. It resolves a difference among literature and shows clearly that the effect of quantum fluctuations may qualitatively change a result obtained by the mean-field theories on lower-dimensional systems.