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The critical properties of the spin-1 two-dimensional Blume-Capel model ondirected and undi- rected random lattices with quenched connectivity disorderis studied through Monte Carlo simulations. The critical temperature, as wellas the critical point exponents are obtained. For the undi- rected case thisrandom system belongs to the same universality class as the regulartwo-dimensional model. However, for the directed random lattice one has asecond-order phase transition for q < qc and a first-order phase transition forq > qc, where qc is the critical rewiring probability. The critical exponentsfor q < qc was calculated and they do not belong to the same universality classas the regular two-dimensional ferromagnetic model.

Blume-Capel model on directed and undirected Small-World Voronoi-Delaunay random lattices