Functional RG approach to the Potts model

TL;DR

This paper applies functional renormalization group techniques to analyze the critical behavior of the Potts model across various dimensions and states, providing a unified method to compute critical exponents.

Contribution

It introduces a general method to derive beta functions for continuous dimensions and states, and computes critical exponents aligning well with existing results.

Findings

Critical exponents agree with Monte Carlo and epsilon-expansion results

Method effectively analyzes percolation and spanning forest universality classes

Convergence is faster in higher dimensions for specific classes

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 $\beta$-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.