Observe vortex (+1) and antivortex (−1) defects emerging and annihilating via Kosterlitz-Thouless physics
1.00
5
On
Vortices (+1): 0
Antivortices (−1): 0
Energy: —
XY Model: each lattice site holds a 2D unit spin (angle θ ∈ [0, 2π)). The Hamiltonian is H = −J Σ cos(θᵢ − θⱼ) over nearest neighbors. Spins prefer to align, but thermal fluctuations create disorder.
Topological defects are vortices: closed loops where the spin angle winds by ±2π. Vortices (+1, shown in red) and antivortices (−1, shown in blue) are topologically protected — they can only be created or destroyed in pairs.
The Kosterlitz-Thouless transition (2016 Nobel Prize) occurs when bound vortex-antivortex pairs unbind at T_KT ≈ 0.89 J/k, driving a phase transition without conventional order parameter. Above T_KT, free vortices proliferate; below, they bind into pairs.