New renormalization equations for the Kosterlitz-Thouless transition

A new set of renormalization equations for the two-dimensional Coulomb gas is derived and solved numerically. These equations give a new picture of the Kosterlitz-Thouless transition. A new temperature T* is found. Above T* the value of the dielectric constant at the transition is εc=1/(4Tc) as before whereas below T* the new result εc1/(4Tc) is obtained. The singular behavior at T* is explored. The results are translated into a renormalization-group flow diagram. An interesting consequence is that the universal jump prediction for the Kosterlitz-Thouless transition turns into a nonuniversal jump prediction for critical temperatures below T*.