  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.
