Order by disorder, without order, in a two-dimensional spin system with O(2) symmetry

TL;DR

This paper rigorously proves an ordering transition in a 2D antiferromagnet with O(2) symmetry, showing local order without overall magnetic order, using a novel 'order by disorder' method based on spin-wave spectra.

Contribution

It provides a rigorous mathematical proof of an 'order by disorder' phenomenon in a 2D spin system with continuous symmetry, highlighting local order emergence without global magnetic order.

Findings

Existence of a low-temperature ordered phase with local order

No overall magnetic order due to Mermin-Wagner theorem

Method employing spin-wave spectra to lift ground state degeneracy

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.