  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.
