XY Model — Vortex/Antivortex Annihilation
Topological defects in the XY model — creation, motion, and annihilation of ±1 vortices
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.