Topological Lattice Actions for the 2d XY Model

Understand

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.
• Thus our study underscores the robustness of universality, which persists even when basic principles of classical physics are violated.