The renormalization equations are the same as those for the Kosterlitz-Thouless transition of the 2D classical XY model [17-19].
When [y.sub.2] is small, the equations reduce to those of the conventional sine-Gordon model (Kosterlitz-Thouless transition).
This may lead to a generalization of the Kosterlitz-Thouless transition, the crossover phenomenon in the Kondo effect, and other phenomena.
Liu, "Localization and the
Kosterlitz-Thouless transition in disordered graphene," Physical Review Letters, vol.
Of particular interest is a special kind of temperature-dependent transition, known as the Kosterlitz-Thouless transition, found in the X-Y model's behavior.
The Kosterlitz-Thouless transition shows up as an abrupt resistance shift at a critical temperature.