Flory exponents from a self-consistent renormalization group

The wandering exponent $\nu$ for an isotropic polymer is predicted remarkably well by a simple argument due to Flory. By considering oriented polymers living in a one-parameter family of background tangent fields, we are able to relate the wandering exponent to the exponent in the background field through an $\epsilon$-expansion. We then choose the background field to have the same correlations as the individual polymer, thus self-consistently solving for $\nu$. We find $\nu = 3/(d + 2)$ for $d < 4$ and $\nu = 1/2$ for $d \ge 4$, which is exactly the Flory result