XY Model & VorticesA sheet of tiny compass needles, each nudging its neighbours to point the same way while heat stirs them. There is no clean freezing point — instead the disorder is carried by whirlpools. Cold, every clockwise whirl is chained to a counter-clockwise one. Warm it past a threshold and the pairs snap, whirlpools wander free, and long-range order dissolves.The energy only cares about angle differences, so in 2D thermal waves forbid true alignment. Kosterlitz and Thouless (1973) realised the real actor is the vortex: bound pairs below T ≈ 0.89, an unbinding “infinite-order” transition above — a topological phase change, and a Nobel Prize in 2016.