  We reexamine the two-dimensional linear O(2) model ($\varphi^4$ 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 $\eta(\Tkt)\simeq 0.24$ and the stiffness jump $\rho_s(\Tkt^-)\simeq
0.64$ at the transition temperature $\Tkt$, in very good agreement with the
exact results $\eta(\Tkt)=1/4$ and $\rho_s(\Tkt^-)=2/\pi$, as well as an
essential singularity of the correlation length in the high-temperature phase
as $T\to \Tkt$.
