Estimation of the order parameter exponent of critical cellular automata using the enhanced coherent anomaly method.

TL;DR

This paper applies the enhanced coherent anomaly method to estimate the critical order parameter exponent of Rule 18 cellular automaton, demonstrating a reliable approach using moderate-sized clusters.

Contribution

It introduces an application of the enhanced coherent anomaly method to cellular automata for estimating critical exponents, providing a new approach in this domain.

Findings

Estimated the critical exponent $eta$ reliably

Used moderate-sized clusters ($n extless= 7$)

Validated the effectiveness of the enhanced coherent anomaly method

Abstract

The stochastic cellular automaton of Rule 18 defined by Wolfram [Rev. Mod. Phys. 55 601 (1983)] has been investigated by the enhanced coherent anomaly method. Reliable estimate was found for the $\beta$ critical exponent, based on moderate sized ($n \le 7$) clusters.