The BKT transition is a topological phase transition in 2D systems (e.g. thin film superfluids, XY spin model). Below T_BKT, vortex-antivortex pairs are bound and the system shows quasi-long-range order. Above T_BKT, pairs unbind and free vortices proliferate, destroying order.
Vortex winding number n = ±1. The interaction energy between a vortex pair separated by r is E ≈ 2πJ ln(r/a). Free vortices screen this logarithmic interaction, producing exponential correlation decay.
This transition earned Kosterlitz and Thouless the 2016 Nobel Prize in Physics.