Three-State Anti-ferromagnetic Potts Model in Three Dimensions: Universality and Critical Amplitudes

Abstract

We present the results of a Monte Carlo study of the three-dimensional anti-ferromagnetic 3-state Potts model. We compute various cumulants in the neighbourhood of the critical coupling. The comparison of the results with a recent high statistics study of the 3D XY model strongly supports the hypothesis that both models belong to the same universality class. From our numerical data for the anti-ferromagnetic 3-state Potts model we obtain for the critical coupling $\coup_c=0.81563(3)$, and for the static critical exponents $γ/ν=1.973(9)$ and $ν=0.664(4)$.