2D XY model: vortex-antivortex binding drives a topological phase transition
T=0.80 Vortex pairs: — Helicity: —
The 2D XY model has spins with continuous angles on a lattice. The Kosterlitz-Thouless transition (T_KT ≈ 0.89J/k_B) is topological: below T_KT, vortex-antivortex pairs are bound and the system has quasi-long-range order; above T_KT, free vortices proliferate, destroying order. Nobel Prize 2016 (Kosterlitz, Thouless, Haldane).