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In many continuous spin systems, competing interactions give nontrivial degeneracies of the classical ground states. Degeneracy-breaking free-energy terms arise from thermal (or quantum) fluctuations, which select for collinear states, and from dilution, which selects for anticollinear (yet long-range ordered) states. They are explicitly computed for an XY square-lattice antiferromagnet dominated by second-neighbor antiferromagnetic exchange. The predicted phase diagram agrees qualitatively with simulations.
Christopher L. Henley (Mon,) studied this question.