Abstract.
We present a rigorous proof of an ordering transition for a two-component two-dimensional antiferromagnet with nearest and next-nearest neighbor interactions. The low-temperature phase contains two states distinguished by local order among columns or, respectively, rows. Overall, there is no magnetic order in accord with the classic Mermin-Wagner theorem. The method of proof employs a rigorous version of “order by disorder,” whereby a high degeneracy among the ground states is lifted according to the differences in their associated spin-wave spectra.
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Communicated by Jennifer Chayes
submitted 07/10/03, accepted 28/04/04
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Biskup, M., Chayes, L. & Kivelson, S.A. Order by Disorder, without Order, in a Two-Dimensional Spin System with O(2) Symmetry. Ann. Henri Poincaré 5, 1181–1205 (2004). https://doi.org/10.1007/s00023-004-0196-2
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DOI: https://doi.org/10.1007/s00023-004-0196-2