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Topological lattice actions for the 2d XY model

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Abstract

We consider the 2d XY Model with topological lattice actions, which are invariant against small deformations of the field configuration. These actions constrain the angle between neighbouring spins by an upper bound, or they explicitly suppress vortices (and anti-vortices). Although topological actions do not have a classical limit, they still lead to the universal behaviour of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition — at least up to moderate vortex suppression. In the massive phase, the analytically known Step Scaling Function (SSF) is reproduced in numerical simulations. However, deviations from the expected universal behaviour of the lattice artifacts are observed. In the massless phase, the BKT value of the critical exponent ηc is confirmed. Hence, even though for some topological actions vortices cost zero energy, they still drive the standard BKT transition. In addition we identify a vortex-free transition point, which deviates from the BKT behaviour.

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Authors and Affiliations

  1. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. P. 70-543, C. P. 04510, Distrito Federal, Mexico

    W. Bietenholz & F. G. Rejón-Barrera

  2. Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012, Bern, Switzerland

    M. Bögli, F. Niedermayer & U.-J. Wiese

  3. Institute for Theoretical Physics - HAS, Eötvös University, Pázmány sétány 1/a, 1117, Budapest, Hungary

    F. Niedermayer

  4. INFN, Sezione di Milano-Bicocca, Edificio U2, Piazza della Scienza 3, 20126, Milano, Italy

    M. Pepe

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  1. W. Bietenholz
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ArXiv ePrint: 1212.0579

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Bietenholz, W., Bögli, M., Niedermayer, F. et al. Topological lattice actions for the 2d XY model. J. High Energ. Phys. 2013, 141 (2013). https://doi.org/10.1007/JHEP03(2013)141

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