Kosterlitz–Thouless transitions is described as a dissociation of bound vortex pairs with opposite circulations, called vortex–antivortex pairs, first described by Vadim Berezinskii. In these systems, thermal generation of vortices produces an even number of vortices of opposite sign. Bound vortex–antivortex pairs have lower energies than free vortices, but have lower entropy as well. In order to minimize free energy, F = E − − T S , the system undergoes a transition at a critical temperature, T c . Below T c , there are only bound vortex–antivortex pairs. Above T c , there are free vortices.