Vortices in the XY Model

BKT transition: topological defects (vortex/anti-vortex pairs) bind/unbind at TBKT

0.50
32
5
T=0.50 J — Below T_BKT≈0.89 J: vortex-antivortex pairs remain bound. Above: free vortices proliferate, destroying quasi-long-range order.