Abstract
We prove that, for spin systems with a continuous symmetry group on lattices of arbitrary dimension, the surface tension vanishes at all temperatures. For the classicalXY model in zero magnetic field, this result is shown to imply absence of interfaces in the thermodynamic limit, at arbitrary temperature. We show that, at values of the temperature at which the free energy of that model is continuously differentiable, i.e. at all except possibly countably many temperatures, there iseither aunique translation-invariant equilibrium state, or all such states are labelled by the elements of the symmetry group, SO(2). Moreover, there areno non-translation-invariant, but periodic equilibrium states. We also reconsider the representation of theXY model as a gas of spin waves and vortices and discuss the possibility that, in four or more dimensions, translation invariance may be broken by imposing boundary conditions which force an (open) vortex sheet through the system. Among our main tools are new correlation inequalities.
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Communicated by A. Jaffe
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Fröhlich, J., Pfister, CE. Spin waves, vortices, and the structure of equilibrium states in the classicalXY model. Commun.Math. Phys. 89, 303–327 (1983). https://doi.org/10.1007/BF01214657
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DOI: https://doi.org/10.1007/BF01214657