Contact process with mobile disorder

Abstract

I study the absorbing-state phase transition in the contact process (CP) with mobile disorder [1]. In this model the dilution sites, though permanently inactive, diffuse freely, exchanging positions with the other sites, which host a basic contact process. This model should be pertinent to experiments on nonequilibrium critical phenomena in media with diffusing impurities. A Harris-like argument suggests that such diffusing disorder is relevant in the case of the CP, which belongs to the universality class of directed percolation (DP). Simulations reveal that the critical creation rate increases with the vacancy density v and diverges at a value v_c < 1, depending on the vacancy diffusion rate. In one dimension, the scaling behavior along this critical line well characterized, and appears to be compatible with that of the diffusive epidemic process (DEP) with equal diffusion rates [2]. For smaller vacancy concentrations, several aspects of scaling appear to be anomalous, and critical exponents appear to vary with the diffusion rate, perhaps reflecting a crossover between the DP and DEP universality classes.

1. R. Dickman, J. Stat Mech. 2009, P08016.

2. R. Kree, B. Schaub, and B. Schmittmann, Phys. Rev. A 39, 2214 (1989).

 

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