Contact process with mobile disorder

I study scaling properties of the absorbing-state phase transition in the one-dimensional contact process with mobile disorder via numerical simulation and the pair approximation. In this model, the dilution sites are permanently inactive but are free to diffuse, exchanging positions with the other sites, which host a basic contact process. Even though the disorder variables are not quenched, the critical behavior is drastically affected: the critical exponent $\delta$ and the ratio $\beta/nu_\perp$ are found to vary continuously with vacancy concentration and hopping rate. At the critical point, the mean lifetime $\tau$ scales with system size $L$ as $\tau \sim (\ln L)^\zeta $, rather than as a power law; the anomalous scaling of the lifetime is associated with fluctuations in the vacancy density.