Griffiths phase for quenched disorder in timescales

Abstract

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 [Formula: see text], only if any neighbor is infected independent of their own state. The type [Formula: see text] sites, once infected recover after [Formula: see text] time-steps and become susceptible at [Formula: see text] time-step. If susceptible, type [Formula: see text] sites are infected with probability [Formula: see text], if any neighbor is infected. The model shows a continuous phase transition from the fluctuating phase to the absorbing phase at [Formula: see text]. The model belongs to the directed percolation universality class for small [Formula: see text]. For larger values of [Formula: see text], 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 [Formula: see text] in the absorbing phase. This region of generic power laws is known as the Griffiths phase. For [Formula: see text], the fraction of infected sites saturates. The local persistence [Formula: see text] 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.