Topological Defects — XY Model Vortices

2D XY model: vortex (+1) and antivortex (−1) defects, BKT transition

Vortices: 0 Antivortices: 0 Pairs: 0 T_BKT ≈ 0.89
About: The 2D XY model has spins θ(i,j) ∈ [0,2π) coupled by H = −J Σ cos(θᵢ−θⱼ). Topological defects (vortices) carry winding number ±1. Below T_BKT ≈ 0.89J/k_B, vortex-antivortex pairs are bound; above it they unbind — the Berezinskii-Kosterlitz-Thouless transition, destroying quasi-long-range order. Red = vortex (+1), blue = antivortex (−1).