Functional RG approach to the Potts model

Abstract

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 β-functions for continuous 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 ϵ-expansion results available in the literature. In particular, we focus on Percolation (n → 0) and Spanning Forest (n→-1) which are the only non-trivial universality classes in d = 4,5 and where our methods converge faster.