Topological Defect Vortex Pair Annihilation
XY model — order parameter field with ±1 vortex pairs
Topological defects in the XY model are point-like vortices where the order parameter (a 2D unit vector field φ) winds by ±2π around a loop encircling the defect. The winding number (topological charge) is conserved: defects can only be created or annihilate in ±1 pairs. This visualization shows the angle field θ(x,y) with color encoding the local orientation, and arrows showing the spin directions. Vortex (+1) and antivortex (−1) pairs attract and annihilate via gradient-driven dynamics. This process underlies the BKT (Berezinskii–Kosterlitz–Thouless) phase transition in 2D — below T_BKT, vortices are bound in pairs; above it, they proliferate and destroy quasi-long-range order.