  The Kosterlitz-Thouless phase transition is described by the nonperturbative
renormalization flow of the two dimensional $\phi^4$-model. The observation of
essential scaling demonstrates that the flow equation incorporates
nonperturbative effects which have previously found an alternative description
in terms of vortices. The duality between the linear and nonlinear
$\sigma$-model gives a unified description of the long distance behaviour for
O(N)-models in arbitrary dimension $d$. We compute critical exponents in first
order in the derivative expansion.
