2D XY Model — Vortex-Antivortex & KT Transition
Topological defect unbinding at the Kosterlitz-Thouless temperature
Vortices: — | Helicity: —
The 2D XY model has spins S_i = (cos θ_i, sin θ_i) with H = −J Σ cos(θ_i − θ_j).
Below T_KT ≈ 0.89J/k_B: vortex-antivortex pairs remain bound — algebraic (quasi-long-range) order.
Above T_KT: pairs unbind and free vortices proliferate — exponential decay of correlations.
Colors show spin angle θ; red/blue circles mark vortices (+1) and antivortices (−1).