Vortex-antivortex pair binding and unbinding
The KT transition (Nobel 2016) is a topological phase transition in 2D: below T_KT, vortex (+) and antivortex (−) pairs are bound — separated only by a finite distance. Above T_KT, thermal energy overcomes the logarithmic binding energy E ~ πJ ln(r/a), and pairs unbind, destroying quasi-long-range order. The correlation function changes from power-law to exponential decay.