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We present a rigorous proof of an ordering transition for a two-componenttwo-dimensional antiferromagnet with nearest and next-nearest neighborinteractions. The low-temperature phase contains two states distinguished bylocal order among columns or, respectively, rows. Overall, there is no magneticorder in accord with the classic Mermin-Wagner theorem. The method of proofemploys a rigorous version of "order by disorder," whereby a high degeneracyamong the ground states is lifted according to the differences in theirassociated spin-wave spectra.Comment: 22 pages, 1 eps fi

Order by Disorder, without Order, in a Two-Dimensional Spin System with O(2) Symmetry