Application of a renormalization group algorithm to nonequilibrium cellular automata with one absorbing state

TL;DR

This paper enhances a renormalization group algorithm for nonequilibrium cellular automata with an absorbing state by incorporating spatial correlations, leading to more accurate modeling of these complex systems.

Contribution

The authors introduce a new approximation scheme that accounts for spatial correlations in the stationary distribution, improving the existing renormalization group method.

Findings

Enhanced accuracy in modeling cellular automata with absorbing states

Effective incorporation of spatial correlations in the renormalization process

Validated approach on a known probabilistic cellular automaton

Abstract

We improve a recently proposed dynamically driven renormalization group algorithm for cellular automata systems with one absorbing state, introducing spatial correlations in the expression for the transition probabilities. We implement the renormalization group scheme considering three different approximations which take into account correlations in the stationary probability distribution. The improved scheme is applied to a probabilistic cellular automaton already introduced in the literature.