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We study the properties of spin systems realized by cold polar molecules interacting via dipole-dipole interactions in two dimensions. Using a spin wave theory, that allows for the full treatment of the characteristic long-distance tail of the dipolar interaction, we find several anomalous features in the ground state correlations and the spin wave excitation spectrum, which are absent in their counterparts with short-range interaction. The most striking consequence is the existence of true long-range order at finite temperature for a two-dimensional phase with a broken U(1) symmetry.
Peter et al. (Wed,) studied this question.