Griffiths phase for quenched disorder in timescales

Priyanka D. Bhoyar and Prashant M. Gade ()
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Priyanka D. Bhoyar: Department of Physics, SK Porwal College, RTM Nagpur University, Kamptee, Nagpur, India
Prashant M. Gade: Department of Physics, RTM Nagpur University, Nagpur, India

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 05, 1-10

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 p, only if any neighbor is infected independent of their own state. The type B sites, once infected recover after Ï„ time-steps and become susceptible at (Ï„+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 Ï„. For larger values of Ï„=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.

Keywords: Griffiths phase; persistence; contact process; directed percolation; temporal quenched disorder (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0129183124500529

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