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

2003/10/31 by Marek Biskup, Lincoln Chayes, Steven A. Kivelson
Physics and Astronomy · Mathematics · #math-ph #cond-mat.stat-mech #math.MP #math.PR #msc:82B05 #msc:82B26 #msc:60F10

paper · pdf · doi:10.1007/s00023-004-0196-2

published as Ann. Henri Poincaré 5 (2004), no. 6, 1181-1205 · 22 pages, 1 eps fig

arxiv created 2004/05/07 · arxiv updated 2009/12/01

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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