We investigate the $O\left(N\right)$ symmetric linear $\sigma$ model in two dimensions by means of an exact nonperturbative evolution equation. The perturbative infrared divergences are absent in this formulation. We use a simple approximative solution of the flow equation which corresponds to a derivative expansion for the effective action. For $N=2\mathrm{}$ this gives a good picture of the Kosterlitz-Thouless phase transition.

• Received 11 October 1994

DOI:https://doi.org/10.1103/PhysRevLett.75.378