Semi-vortices and cluster-vorticity: new concepts in the Berezinskii-Kosterlitz-Thouless phase transition

TL;DR

This paper introduces new concepts of semi-vortices and cluster vorticity to better understand the Berezinskii-Kosterlitz-Thouless phase transition in the 2d XY model, providing a potential new criterion for criticality.

Contribution

It proposes and investigates semi-vortices and cluster vorticity as novel quantitative criteria for the BKT transition, using multi-cluster algorithms.

Findings

New criterion based on semi-vortices and cluster vorticity

Enhanced understanding of BKT transition mechanisms

Simulation results support the proposed criteria

Abstract

The Berezinskii-Kosterlitz-Thouless (BKT) essential phase transition in the 2d XY model is revisited. Its mechanism is usually described by the (un)binding of vortex--anti-vortex (V--AV) pairs, which does, however, not provide a clear-cut quantitative criterion for criticality. Known sharp criteria are the divergence of the correlation length and a discontinuity of the helicity modulus. Here we propose and probe a new criterion: it is based on the concepts of semi-vortices and cluster vorticity, which are formulated in the framework of the multi-cluster algorithm that we use to simulate the 2d XY model.