Blume–Capel model on directed and undirected small-world Voronoi–Delaunay random lattices

The critical properties of the spin-1 two-dimensional Blume–Capel model on directed and undirected random lattices with quenched connectivity disorder is studied through Monte Carlo simulations. The critical temperature, as well as the critical point exponents are obtained. For the undirected case this random system belongs to the same universality class as the regular two-dimensional model. However, for the directed   random lattice one has a second-order phase transition for qqcq>qc, where qcqc is the critical rewiring probability. The critical exponents for q