Persistence in the Zero-Temperature Dynamics of the Random Ising Ferromagnet on a Voronoi-Delaunay lattice

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The zero-temperature Glauber dynamic is used to investigate the persistence probability P(t) in the randomic two-dimensional ferromagnetic Ising model on a Voronoi-Delaunay tessellation. We consider the coupling factor J varying with the distance r between the first neighbors to be J(r) ∝ e⁻αʳ, with α≥ 0. The persistence probability of spins flip, that does not depends on time t, is found to decay to a non-zero value P(∞) depending on the parameter α. Nevertheless, the quantity p(t)=P(t)-P(∞) decays exponentially to zero over long times. Furthermore, the fraction of spins that do not change at a time t is a monotonically increasing function of the parameter α. Our results are consistent with the ones obtained for the diluted ferromagnetic Ising model on a square lattice.