  We determined the critical exponent $\nu$ of the scalar O(N) model with a
strategy based on the definition of the correlation length in the infrared
limit. The functional renormalization group treatment of the model shows that
there is an infrared fixed point in the broken phase. The appearing degeneracy
induces a dynamical length scale there, which can be considered as the
correlation length. It is shown that the IR scaling behavior can account either
for the Ising type phase transition in the 3-dimensional O(N) model, or for the
Kosterlitz-Thouless type scaling of the 2-dimensional O(2) model.
