Nonperturbative renormalization flow and essential scaling for the Kosterlitz-Thouless transition

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 that 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 behavior for $O\left(N\right)\mathrm{}$ models in arbitrary dimension d. We compute critical exponents in first order in the derivative expansion.