XY model: planar spins S = (cos θ, sin θ) with energy H = −J∑cos(θᵢ−θⱼ). Vortices (topological charge +1) and antivortices (−1) are metastable defects. Below the Berezinskii-Kosterlitz-Thouless temperature T_BKT, opposite-charge pairs are bound. Above T_BKT, they unbind and proliferate — driving the KT phase transition, which has no symmetry breaking (no order parameter) despite a genuine phase change.