In this work we show how one can use the zeros of the canonical partition function, the Fisher zeros, to unambiguously characterize a transition as being in the Berezinskii-Kosterlitz-Thouless (
BKT) class of universality. By studying the zeros map for the 2D XY-model, we found that its internal border coalesces into the real positive axis in a finite region corresponding to temperatures smaller than the
BKT transition temperature. This behavior is consistent with the predicted existence of a line of critical points below the transition temperature, allowing one to distinguish the
BKT class of universality from other possibilities.
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.