A Monte Carlo investigation of the critical behavior of Stavskaya's probabilistic cellular automaton

TL;DR

This paper uses Monte Carlo simulations and finite-size scaling to analyze Stavskaya's probabilistic cellular automaton, confirming its phase transition belongs to the directed percolation universality class and establishing a new connection with the Domany-Kinzel PCA.

Contribution

It provides the first detailed numerical characterization of Stavskaya's PCA critical behavior and links it to the Domany-Kinzel PCA, expanding understanding of nonequilibrium phase transitions.

Findings

Critical exponents match directed percolation universality class.

Confirmed phase transition is of the directed percolation type.

Established explicit relationship with Domany-Kinzel PCA.

Abstract

Stavskaya's model is a one-dimensional probabilistic cellular automaton (PCA) introduced in the end of the 1960's as an example of a model displaying a nonequilibrium phase transition. Although its absorbing state phase transition is well understood nowadays, the model never received a full numerical treatment to investigate its critical behavior. In this short article we characterize the critical behavior of Stavskaya's PCA by means of Monte Carlo simulations and finite-size scaling analysis. The critical exponents of the model are calculated and indicate that its phase transition belongs to the directed percolation universality class of critical behavior, as it would be expected on the basis of the directed percolation conjecture. We also explicitly establish the relationship of the model with the Domany-Kinzel PCA on its directed site percolation line, a connection that seems to have gone unnoticed in the literature so far.