An electric-field representation of the harmonic XY model

Michael F. Faulkner, Steven T. Bramwell and Peter C. W. Holdsworth

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The harmonic XY (HXY) model is a lattice phase (or spin) model in which the classical phases interact via a piecewise parabolic interaction. In this paper, we presented a theory of the HXY model as a phase-model analogue of the two-dimensional electrolyte of Phys. Rev. B 91, 155412. While the electrolyte is an excellent model for investigating the mechanics of the BKT transition, it is a less realistic model of superfluid and superconducting condensate films and layers than the HXY model as its charges cannot be described as vortices in a phase field. We used our theory to explain how the HXY model recreates the high-temperature specific heat of condensates, and why this is strikingly different from that of the electrolyte. We then mapped the topological sectors of the electrolyte to global HXY condensate-phase twists, which may explain the nonergodicity in the condensate-phase field measured in layered cuprates at the superconducting transition Paper accepted with zero revisions.