2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57518We 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.22 pages, 1 eps figMathematical PhysicsStatistical MechanicsProbability82B05; 82B26; 60F10text