2D XY Model — Vortex-Antivortex & KT Transition

Kosterlitz-Thouless transition via vortex pair unbinding — topological order below T_KT

Controls

KT transition T_KT ≈ 0.89J
Below T_KT: bound vortex-antivortex pairs — quasi-long-range order
Above T_KT: free vortices proliferate — exponential decay

Vortex charge: q = (1/2π)∮∇θ·dl = ±1