  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 $J(r) \propto
e^{-\alpha r}$, with $\alpha \ge 0$. The persistence probability of spins flip,
that does not depends on time $t$, is found to decay to a non-zero value
$P(\infty)$ depending on the parameter $\alpha$. Nevertheless, the quantity
$p(t)=P(t)-P(\infty)$ 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 $\alpha$. Our results are
consistent with the ones obtained for the diluted ferromagnetic Ising model on
a square lattice.

Statistical Mechanics