Abstract
We investigate the $O(N)$ symmetric linear $\ensuremath{\sigma}$ 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 $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ this gives a good picture of the Kosterlitz-Thouless phase transition.
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