XY Model — Vortex/Antivortex Annihilation

Topological defects in the XY model — creation, motion, and annihilation of ±1 vortices

Vortices: 0
Energy: 0
The XY model has a U(1) symmetry: each spin is a planar angle θᵢ. Vortices are topological defects where the angle winds by ±2π around a loop — they cannot be removed by local updates. Above the BKT temperature, free vortices proliferate. Below it, they bind into pairs. Click to inject a vortex-antivortex pair. Watch them attract and annihilate with a burst of spin waves.