XY model: H = −J Σ cos(θᵢ − θⱼ), where θᵢ ∈ [0, 2π) is the spin angle at each site. Vortices are topological defects with winding number ±1 — the angle winds ±2π around the defect core. The Berezinskii-Kosterlitz-Thouless (BKT) transition at T_BKT ≈ 0.89J is driven by vortex-antivortex unbinding, not conventional symmetry breaking. It is a topological phase transition with no local order parameter — a Nobel Prize-winning discovery (Kosterlitz, Thouless, 2016).