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Critical behavior of the absorbing state transition in the contact process with relaxing immunization


  • Cruz, Claudia P.T.
  • Lyra, M.L.
  • Fulco, U.L.
  • Corso, Gilberto


We introduce a model for the Contact Process with relaxing immunization CPRI. In this model, local memory is introduced by a time and space dependence of the contamination probability. The model has two parameters: a typical immunization time τ and a maximum contamination probability a. The system presents an absorbing state phase transition whenever the contamination probability a is above a minimum threshold. For short immunization times, the system evolves to a statistically stationary active state. Above τc(a), immunization predominates and the system evolves to the absorbing vacuum state. We employ a finite-size scaling analysis to show that the transition belongs to the standard directed percolation universality class. The critical immunization time diverges in the limit of a→1. In this regime, the density of active sites decays exponentially as τ increases, but never reaches the vacuum state in the thermodynamic limit.

Suggested Citation

  • Cruz, Claudia P.T. & Lyra, M.L. & Fulco, U.L. & Corso, Gilberto, 2012. "Critical behavior of the absorbing state transition in the contact process with relaxing immunization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5349-5354.
  • Handle: RePEc:eee:phsmap:v:391:y:2012:i:22:p:5349-5354
    DOI: 10.1016/j.physa.2012.05.066

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