Griffiths phase for quenched disorder in timescales

In contact processes, the population can have heterogeneous recovery rates for various reasons. We introduce a model of the contact process with two coexisting agents with different recovery times. Type A sites are infected with probability p, only if any neighbor is infected independent of their own state. The type B sites, once infected recover after τ time-steps and become susceptible at (τ+1)th time-step. If susceptible, type B sites are infected with probability p, if any neighbor is infected. The model shows a continuous phase transition from the fluctuating phase to the absorbing phase at p=pc. The model belongs to the directed percolation universality class for small τ. For larger values of τ=8,16, the model belongs to the activated scaling universality class. In this case, the fraction of infected sites of either type shows a power-law decay over a range of infection probability ppc, the fraction of infected sites saturates. The local persistence Pl(t) also shows a power-law decay with continuously changing exponent for either type of agent. Thus, the quenched disorder in timescales can lead to the temporal Griffiths phase in models that show a transition to an absorbing state.