The Berezinskii-Kosterlitz-Thouless transition in the 2D XY model. Below T_BKT ≈ 0.89 J/k_B, vortex-antivortex pairs are bound. Above T_BKT they unbind, destroying quasi-long-range order. Color shows phase angle θ ∈ [0,2π); arrows show local spin direction.