Continuous phase transition in a disordered eight-states Potts model

We investigate the two-dimensional eight-states ferromagnetic Potts model in the Voronoi-Delaunay tessellation. In this study, we assume that the coupling factor J varies with the distance r between the first neighbors as \(\), with \(\). The disordered system is simulated applying the single-cluster Monte-Carlo update algorithm and the reweighting technique. We find that this model displays a first-order phase transition if \(\), in agreement with previous recent studies. For \(\)and 1.0, a typical second order transition is observed and the critical exponents for magnetization and susceptibility are calculated.