Kosterlitz–Thouless Transition — Vortex Unbinding

The KT transition (2016 Nobel Prize) is a phase transition driven by topological defects (vortex-antivortex pairs) in 2D XY systems. Below T_KT pairs are bound; above T_KT they unbind, destroying quasi-long-range order. The XY model evolves via Langevin dynamics with vortex pair dynamics visualized.

Parameters

Temperature T/J 0.8 Speed (sweeps/frame) 5

Stats

T_KT ≈ 0.89J

Free vortices: 0

⟨cos(Δθ)⟩: —

Helicity ϒ: —

Color = spin angle θ ∈ [0, 2π)
Red dot = +1 vortex
Blue dot = −1 antivortex
T < T_KT: bound pairs
T > T_KT: free vortices proliferate