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

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We reexamine the two-dimensional linear O(2) model (φ⁴ 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 η()≃ 0.24 and the stiffness jump ρₛ(-)≃ 0.64 at the transition temperature, in very good agreement with the exact results η()=1/4 and ρₛ(-)=2/π, as well as an essential singularity of the correlation length in the high-temperature phase as T→.