Numerical study of persistence in systems with absorbing states

Extensive Monte Carlo simulations are performed in order to evaluate both the local ($\theta_{l}$) and global ($\theta_{g}$) persistence exponents in the Ziff-Gulari-Barshad (ZGB) (Phy. Rev. Lett. {\bf 56}, 2553, (1986)) irreversible reaction model. In two dimensions and for the second-order irreversible phase transition (IPT) we find, that both the local and the global persistence exhibit power-law behavior with a crossover between two different time regimes. On the other hand, at the first-order IPT, characteristic of the ZGB, active sites are short lived and the persistence decays more abruptly, not being clear whether it shows power law behavior or not. In order to analyze universality issues, we have also studied another model with absorbing states, the contact process, and evaluated the local persistence exponent in dimensions from 1 to 4. A striking apparent {\it super-universality} is reported: the local persistence exponent seems to coincide in both one and two dimensional systems.