Can the Ising critical behavior survive in non-equilibrium synchronous cellular automata?

TL;DR

This study demonstrates that Ising-like critical behavior persists in certain two-dimensional synchronously updated probabilistic cellular automata, showing robustness against anisotropy and synchronism effects.

Contribution

It reveals that synchronous Glauber PCAs belong to the Ising universality class, and majority-vote PCAs exhibit exponents close to Ising, challenging previous beliefs about non-Ising classes.

Findings

Synchronous Glauber PCAs are in the Ising class regardless of anisotropy.

Majority-vote PCAs have exponents near the Ising value with slight anisotropy dependence.

No known PCAs exhibit non-Ising critical behavior under studied conditions.

Abstract

Universality classes of Ising-like phase transitions are investigated in series of two-dimensional synchronously updated probabilistic cellular automata (PCAs), whose time evolution rules are either of Glauber type or of majority-vote type, and degrees of anisotropy are varied. Although early works showed that coupled map lattices and PCAs with synchronously updating rules belong to a universality class distinct from the Ising class, careful calculations reveal that synchronous Glauber PCAs should be categorized into the Ising class, regardless of the degree of anisotropy. Majority-vote PCAs for the system size considered yield exponents $\nu$ which are between those of the two classes, closer to the Ising value, with slight dependence on the anisotropy. The results indicate that the Ising critical behavior is robust with respect to anisotropy and synchronism for those types of non-equilibrium PCAs. There are no longer any PCAs known to belong to the non-Ising class.