Potts model with q=4,6, and 8 states on Voronoi-Delaunay random lattice

Through Monte Carlo simulations we study the 2D Potts models with q=4,6 and 8 states on Voronoi-Delaunay random lattice. In this study, we assume that the coupling factor J varies with the distance r between the first neighbors as J(r)∝e−ar, with a≥0. The disordered system is simulated by applying the single-cluster Monte Carlo update algorithm and the reweighting technique. In this model both second-order and first-order phase transitions are present depending on q values and a parameter. The critical exponents' ratios β/ν,γ/ν, and 1/ν were calculated for the case where the second-order phase transitions are present. In the Potts model with q=8 we also studied the distribution of cluster sizes.