Assume the case with only vortices of multiplicity ± ± 1 . At low temperatures and large β β the distance between a vortex and antivortex pair tends to be extremely small, essentially of the order 1 / Λ Λ . At large temperatures and small β β this distance increases, and the favoured configuration becomes effectively the one of a gas of free vortices and antivortices. The transition between the two different configurations is the Kosterlitz–Thouless phase transition, and the transition point is associated with an unbinding of vortex-antivortex pairs.