Topological Defects — XY Model (BKT Physics)

The 2D XY model undergoes the Berezinskii-Kosterlitz-Thouless (BKT) transition via topological defect (vortex) unbinding. Above T_BKT, free vortex-antivortex pairs proliferate. Watch +1 vortices (red) and –1 antivortices (blue) annihilate as temperature drops.

Vortices: 0 | Antivortices: 0 | Free pairs: 0
H = −J Σ cos(θᵢ − θⱼ) | Vortex charge q = (1/2π)∮∇θ·dl ∈ ℤ | T_BKT ≈ πJ/2