XY Model: Each spin has angle θ ∈ [0,2π). Energy E = −J Σ cos(θᵢ−θⱼ). Below TKT ≈ 0.89, vortex-antivortex pairs are bound; above, they unbind (Kosterlitz-Thouless transition). Winding number w = (1/2π)∮∇θ·dl around a plaquette: w = ±1 marks a defect. Colors show spin angle. Click canvas to add a vortex.