Topological Defects — Vortices in Superfluid XY Model

In 2D superfluids and the XY model, vortices are topological defects with quantized phase winding ±2π. Below the BKT temperature, vortex-antivortex pairs are bound. Above T_BKT, free vortices proliferate and destroy quasi-long-range order.

Controls

Temperature T/T_BKT 0.70 Lattice size N 20 Sweep steps per frame 50

V+: 0 V−: 0

XY Hamiltonian:
H = −J Σ cos(θᵢ−θⱼ)

Vortex: ∮∇θ·dl = 2πn
n=+1: red | n=−1: blue

BKT transition: vortex pairs unbind at T_BKT ≈ π/2 J.