The 2D XY model — spins free to rotate in a plane — undergoes the Berezinskii-Kosterlitz-Thouless (BKT) transition. Below Tc, vortex-antivortex pairs are bound by a logarithmic interaction; above Tc they unbind, destroying quasi-long-range order. Watch vortices (winding +1, pink) and antivortices (winding -1, cyan) annihilate as the system cools.