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Recently one has stated that temporal disorder constitutes a relevantperturbation in absorbing phase transitions for all dimensions. However, itseffect for systems other than the standard contact process (CP), itscompetition with other ingredients (e.g. particle diffusion) and other kinds ofdisorder (besides the standard types) are unknown. In order to shed some lightin the above mentioned points, we investigate a variant of the usual CP, namelytriplet annihilation model (TAM), in which the competition between tripletannihilation and single particle diffusion leads to an unusual phase diagrambehavior, with reentrant shape and endless activity for sufficient largediffusion rates. Two kinds of time-dependent disorder have been considered. Inthe former, it is introduced in the creation-annihilation parameters (ascommonly considered in recent studies), whereas in the latter the diffusionrate $D$ (so far unexplored) is allowed to be time dependent. In all cases, thedisorder follows an uniform distribution with fixed mean and width $\sigma$.Two values of $\sigma$ have been considered, in order to exemplify the regimeof "weaker" and "stronger" temporal disorder strengths. Our results show thatin the former approach, the disorder suppresses the reentrant phase diagramwith a critical behavior deviating from the directed percolation universalityclass (DP) in the regime of low diffusion rates, while they strongly suggestthat the DP class is recovered for larger hoping rates. An opposite scenario isfound in the latter disorder approach, with a substantial increase of reentrantshape and the maximum diffusion, in which the reentrant shape also displays acritical behavior consistent to the DP universality class (in similarity withthe pure model). Lastly, comparison with the diffusive disordered CP has beenundertaken.

Comparing the influence of distinct kinds of temporal disorder in a low dimensional absorbing transition model