  The critical behavior of the $(n+1)$-states Potts model in $d$-dimensions is
studied with functional renormalization group techniques. We devise a general
method to derive $\beta$-functions for continuos values of $d$ and $n$ and we
write the flow equation for the effective potential (LPA) when instead $n$ is
fixed. We calculate several critical exponents, which are found to be in good
agreement with Monte Carlo simulations and $\epsilon$-expansion results
available in the literature. In particular, we focus on Percolation $(n\to0)$
and Spanning Forest $(n\to-1)$ which are the only non-trivial universality
classes in $d=4,5$ and where our methods converge faster.
