Search

We analyze the absorbing state phase transition exhibited by two distinct unidimensional delayed contact process (CP). The first is characterized by the introduction of an infection period and the second by an immune period in the dynamics of the original model. We characterize these CP by the quantities t d (infection or disease period) and t i (immune period). The quantity t d corresponds to the period interval an individual remains infected after being contaminated, while the period t i is the time interval an individual remains immune after being cured. We used Monte Carlo simulations to compute the critical parameters associated with the absorbing state phase transition exhibited by these models. We find two distinct power-law scale relations for the critical infection rate [Formula: see text] and the critical cure rate [Formula: see text]. For the CP delayed by the minimum infection period we find μd = 0.98, while we obtained μi = 0.80 for the case of a delay due to immunity. In addition, we used a finite-size scaling analysis to estimate the critical exponents β/ν and ν, and found that these models belong to the universality class of directed percolation irrespective to the time delay.

In this work, we extend the recursive search method to locate the critical point and to obtain the relevant critical exponents of a nonequilibrium phase transition. In particular, the method is applied to the contact process which presents a nonequilibrium phase transition between a steady active to a single inactive absorbing state belonging to the directed percolation universality class. We present the appropriate scaling analysis which allows for precise estimates of the critical parameters with a relatively small computational effort. The proposed scheme can be directly applied to general model systems presenting nonequilibrium transitions into absorbing states including reaction–diffusion and pair contact processes.