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

TL;DR

This paper investigates the probability distribution of the order parameter in directed percolation models using Monte Carlo simulations, demonstrating a novel method for analyzing nonequilibrium phase transitions.

Contribution

It introduces a new approach applying probability distribution functions to study criticality in nonequilibrium systems, extending methods from equilibrium statistical mechanics.

Findings

Method successfully identifies critical points in directed percolation models.

Probability distributions reveal universal features of the phase transition.

Approach applicable to other nonequilibrium systems.

Abstract

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.