Topological Lattice Actions for the 2d XY Model

TL;DR

This paper investigates the 2d XY Model with topological lattice actions that suppress vortices, demonstrating that the BKT transition's universal features persist despite violations of classical principles, and identifying a vortex-free transition.

Contribution

The study shows that topological lattice actions, which lack a classical limit, still reproduce the universal BKT transition behavior and identifies a novel vortex-free transition point.

Findings

Reproduces the SSF in the massive phase.

Confirms the BKT critical exponent eta_c.

Identifies a vortex-free transition point.

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. Thus our study underscores the robustness of universality, which persists even when basic principles of classical physics are violated. In the massive phase, the analytically known Step Scaling Function (SSF) is reproduced in numerical simulations. In the massless phase, the BKT value of the critical exponent eta_c 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.