In my previous post about the 2016 Nobel Prize in Physics I stated that the Kosterlitz-Thouless transition was a classical phase transition (involving topological objects = vortices), in contrast to the quantum phase transitions associated with topological phases of matter.
However, on reflection I realised that it should not be overlooked that there is something distinctly quantum about the KT transition. In a two-dimensional superfluid it involves the binding of pairs of vortices and anti-vortices. These each have a quantum of circulation (+/-h/m where h is Planck's constant and m is the particle mass).
At the KT transition temperature Tc there is a finite jump in the superfluid density rho. The value just below Tc is related to Tc by
Note that Planck's constant appears in this equation.
In a classical world (h=0), Tc would be zero and there would be no KT transition!
This universal relation was derived by Nelson and Kosterlitz in 1977
The figure below contains a range of experimental data testing this relation.