Berezinskii-Kosterlitz-Thouless Transition with a Constraint Lattice Action

TL;DR

This study demonstrates that a topological lattice action with a simple angle constraint still exhibits a Berezinskii-Kosterlitz-Thouless transition, confirmed through precise numerical measurements, challenging traditional energy-based interpretations of vortex unbinding.

Contribution

It provides the first detailed numerical evidence of a BKT transition in a topological lattice action without couplings, highlighting the transition's robustness and revealing deviations from standard theoretical predictions.

Findings

BKT transition confirmed in a topological lattice action

Finite size effects are remarkably mild compared to other actions

Vortex unbinding occurs without energy cost, questioning traditional views

Abstract

The 2d XY model exhibits an essential phase transition, which was predicted long ago --- by Berezinskii, Kosterlitz and Thouless (BKT) --- to be driven by the (un)binding of vortex--anti-vortex pairs. This transition has been confirmed for the standard lattice action, and for actions with distinct couplings, in agreement with universality. Here we study a highly unconventional formulation of this model, which belongs to the class of topological lattice actions: it does not have any couplings at all, but just a constraint for the relative angles between nearest neighbour spins. By means of dynamical boundary conditions we measure the helicity modulus Upsilon, which shows that this formulation performs a BKT phase transition as well. Its finite size effects are amazingly mild, in contrast to other lattice actions. This provides one of the most precise numerical confirmations ever of a BKT transition in this model. On the other hand, up to the lattice sizes that we explored, there are deviations from the spin wave approximation, for instance for the Binder cumulant U_4 and for the leading finite size correction to Upsilon. Finally we observe that the (un)binding mechanism follows the usual pattern, although free vortices do not require any energy in this formulation. Due to that observation, one should reconsider an aspect of the established picture, which estimates the critical temperature based on this energy requirement.