Topological lattice actions for the 2d XY model

Bietenholz, W. and Bogli, M. and Niedermayer, Ferenc and Pepe, M. and Rejon-Barrera, F. G. and Wiese, U. J. (2013) Topological lattice actions for the 2d XY model. JOURNAL OF HIGH ENERGY PHYSICS (3). ISSN 1126-6708

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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 ac- tions constrain the angle between neighbouring spins by an upper bound, or they explicitly suppress vortices (and anti-vortices). Although topo- logical 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. Thus our study un- derscores the robustness of universality, which persists even when basic principles of classical physics are violated. In the massive phase, the an- alytically known Step Scaling Function (SSF) is reproduced in numerical simulations. In the massless phase, the BKT value of the critical expo- nent 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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