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Through Monte Carlo simulations we study two-dimensional Potts models with$q=4, 6$ and 8 states on Voronoi-Delaunay random lattice. In this study, weassume that the coupling factor $J$ varies with the distance $r$ between thefirst neighbors as $J(r)\propto e^{-a r}$, with $a \geq 0$ . The disorderedsystem is simulated applying the singler-cluster Monte Carlo update algorithmand reweigting technique. In this model both second-order and first-order phasetransition are present depending of $q$ values and $a$ parameter. The criticalexponents ratio $\beta/\nu$, $\gamma/\nu$, and $1/\nu$ were calculated for casewhere the second-order phase transition are present. In the Potts model with$q=8$ we also studied the distribution of clusters sizes.

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