The 𝑞-state Potts model from the nonperturbative renormalization group.

Abstract

We study the q-state Potts model for q and the space dimension d arbitrary real numbers using the Derivative Expansion of the Nonperturbative Renormalization Group at its leading order, the local potential approximation (LPA and LPA’). We determine the curve qc(d) separating the first (q > qc(d)) and second (q < qc(d)) order phase transition regions for 2.8 < d ≤ 4. At small ϵ = 4 − d and δ = q − 2 the calculation is performed in a double expansion in these parameters and we find qc(d) = 2 + aϵ 2 with a ≃ 0.1. For finite values of ϵ and δ, we obtain this curve by integrating the LPA and LPA’ flow equations. We find that qc(d = 3) = 2.11(7) which confirms that the transition is of first order in d = 3 for the three-state Potts model.