XY Model Vortex Defects

Spins on a 2D lattice with nearest-neighbor alignment. Topological defects (vortices) emerge and interact — the Kosterlitz-Thouless transition drives vortex-antivortex unbinding.

Vortices: — Antivortices: —
KT transition at TKT ≈ 0.89 J/kB.
Below: bound vortex pairs (quasi-LRO).
Above: free vortices proliferate.
Charge: +1 vortex (CCW), -1 antivortex (CW).