ABSTRACT
The Berezinskii-Kosterlitz-Thouless (BKT) transition [1-3] is the finitetemperature transition between superfluid and normal states in two dimensions.∗ A crucial feature of the BKT transition is that it is driven by the statistics of an asymptotically dilute gas of large-size vortex pairs: Up to the very critical point from the superfluid side, the distribution of vortex-antivortex pairs is such that the probability of finding at least one pair with the distance between the two vortices on the order of the linear system size is macroscopically small.† The asymptotically vanishing concentration of the vortex pairs renders BKT transition distinctively different from other second-order superfluid-normal phase transitions, the most specific feature being the fact that the superfluid density remains finite up to the transition point and then jumps to zero (in the thermodynamic limit). This jump in the superfluid density should not be interpreted as a firstorder phase transition, since it comes exclusively from an infinitesimal concentration of free vortices nullifying the static response to the twisted boundary condition (or gauge phase in annulus geometry). The vanishing density of the vortex-antivortex pairs implies that other thermodynamic quantities remain continuous (including all derivatives, as we will see later) across the BKT transition point.
