Vortices and anti-vortices in the 2D XY model annihilate in pairs, driving the Berezinskii-Kosterlitz-Thouless phase transition.
The BKT transition (T_BKT ≈ 0.89 J/k_B) is driven by vortex unbinding: below T_BKT, vortex–antivortex pairs are bound; above, free vortices proliferate and destroy quasi-long-range order. Watch ±1 defects (red/blue) attract and annihilate.