Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition

We reexamine the two-dimensional linear O(2) model (phi(4) theory) in the framework of the nonperturbative renormalization-group. From the flow equations obtained in the derivative expansion to second order and with optimization of the infrared regulator, we find a transition between a high-temperature (disordered) phase and a low-temperature phase displaying a line of fixed points and algebraic order. We obtain a picture in agreement with the standard theory of the Kosterlitz-Thouless (KT) transition and reproduce the universal features of the transition. In particular, we find the anomalous dimension eta(T-KT) similar or equal to 0.24 and the stiffness jump rho(s)(T-KT) similar or equal to 0.64 at the transition temperature T-KT, in very good agreement with the exact results eta(T-KT) = 1/4 and rho(s)(T-KT) = 2/pi, as well as an essential singularity of the correlation length in the high-temperature phase as T -> T-KT.