Topological lattice actions for the 2d XY model

  • W. Bietenholz
  • M. Bögli
  • F. Niedermayer
  • M. Pepe
  • F. G. Rejón-Barrera
  • U.-J. Wiese


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.


Nonperturbative Effects Lattice Quantum Field Theory Field Theories in Lower Dimensions Sigma Models 


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Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • W. Bietenholz
    • 1
  • M. Bögli
    • 2
  • F. Niedermayer
    • 2
    • 3
  • M. Pepe
    • 4
  • F. G. Rejón-Barrera
    • 1
  • U.-J. Wiese
    • 2
  1. 1.Instituto de Ciencias NuclearesUniversidad Nacional Autónoma de MéxicoDistrito FederalMexico
  2. 2.Albert Einstein Center for Fundamental Physics, Institute for Theoretical PhysicsBern UniversityBernSwitzerland
  3. 3.Institute for Theoretical Physics - HASEötvös UniversityBudapestHungary
  4. 4.INFN, Sezione di Milano-BicoccaMilanoItaly

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