Probability distribution of the order parameter in the directed percolation universality class

The probability distributions of the order parameter for two models in the directed percolation universality class were evaluated. Monte Carlo simulations have been performed for the one-dimensional generalized contact process and the Domany-Kinzel cellular automaton. In both cases, the density of active sites was chosen as the order parameter. The criticality of those models was obtained by solely using the corresponding probability distribution function. It has been shown that the present method, which has been successfully employed in treating equilibrium systems, is indeed also useful in the study of nonequilibrium phase transitions.

💡 Research Summary

The paper investigates the full probability distribution of the order parameter in two prototypical models belonging to the directed‑percolation (DP) universality class: the one‑dimensional generalized contact process (GCP) and the Domany‑Kinzel (DK) cellular automaton. In both cases the density of active sites, ρ, is taken as the order parameter. Rather than focusing on its mean value or low‑order moments, the authors compute the entire stationary distribution P(ρ;L,p) for a range of system sizes L (up to 2^12) and control parameters p (infection or transition probability) using extensive Monte‑Carlo simulations (∼10^7 samples per parameter set).

The central result is that near the critical point p_c the distribution obeys a finite‑size scaling form identical to that found in equilibrium critical phenomena:

 P(ρ;L,p) = L^{β/ν⊥} f