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A nonequilibrium Potts-like model with $q$ absorbing states is studied usingMonte Carlo simulations. In two dimensions and $q=3$ the model exhibits adiscontinuous transition. For the three-dimensional case and $q=2$ the modelexhibits a continuous, transition with $\beta=1$ (mean-field). Simulations areinconclusive, however, in the two-dimensional case for $q=2$. We suggest thatin this case the model is close to or at the crossing point of lines separatingthree different types of phase transitions. The proposed phase diagram in the$(q,d)$ plane is very similar to that of the equilibrium Potts model. Inaddition, our simulations confirm field-theory prediction that in twodimensions a branching-annihilating random walk model without parityconservation belongs to the directed percolation universality class.Comment: 8 pages, figures included, accepted in Phys.Rev.

Phase transitions in nonequilibriumd-dimensional models withqabsorbing states