Faulkner, MF;
Bramwell, ST;
Holdsworth, PCW;
(2017)
An electric-field representation of the harmonic XY model.
Journal of Physics: Condensed Matter
, 29
(8)
, Article 085402. 10.1088/1361-648X/aa523f.
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Abstract
The two-dimensional harmonic XY (HXY) model is a spin model in which the classical spins interact via a piecewise parabolic potential. We argue that the HXY model should be regarded as the canonical classical lattice spin model of phase fluctuations in two-dimensional condensates, as it is the simplest model that guarantees the modular symmetry of the experimental systems. Here we formulate a lattice electric-field representation of the HXY model and contrast this with an analogous representation of the Villain model and the two-dimensional Coulomb gas with a purely rotational auxiliary field. We find that the HXY model is a spin-model analogue of a lattice electric-field model of the Coulomb gas with an auxiliary field, but with a temperature-dependent vacuum (electric) permittivity that encodes the coupling of the spin vortices to their background spin-wave medium. The spin vortices map to the Coulomb charges, while the spin-wave fluctuations correspond to auxiliary-field fluctuations. The coupling explains the striking differences in the high-temperature asymptotes of the specific heats of the HXY model and the Coulomb gas with an auxiliary field. Our results elucidate the propagation of effective long-range interactions throughout the HXY model (whose interactions are purely local) by the lattice electric fields. They also imply that global spin-twist excitations (topological-sector fluctuations) generated by local spin dynamics are ergodically excluded in the low-temperature phase. We discuss the relevance of these results to condensate physics.
| Type: | Article |
|---|---|
| Title: | An electric-field representation of the harmonic XY model |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1088/1361-648X/aa523f |
| Publisher version: | https://doi.org/10.1088/1361-648X/aa523f |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | generalized lattice electrostatics, two-dimensional harmonic XY model, twodimensional Coulomb gas, Berezinskii–Kosterlitz–Thouless phase transition, two-dimensional condensates, ergodicity breaking |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1539831 |
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