Finding ground states of a square Newman-Moore lattice with sides equal to a Mersenne number using the Rule 60 cellular automaton

TL;DR

This paper demonstrates how to find all ground states of the classical Newman-Moore model on a square lattice with Mersenne number sides using properties of the Rule 60 cellular automaton, providing a novel analytical approach.

Contribution

It introduces a method leveraging Rule 60 cellular automaton properties to explicitly construct ground states of the Newman-Moore model on Mersenne-sized lattices.

Findings

All ground states can be constructed using the propagator derived from Rule 60.

The number of ground states is half of the total possible configurations per row.

The method applies specifically to lattices with sides equal to Mersenne numbers.

Abstract

We offer detailed proofs of some properties of the Rule 60 cellular automaton on a ring with a Mersenne number circumference. We then use these properties to define a propagator, and demonstrate its use to construct all the ground state configurations of the classical Newman-Moore model on a square lattice of the same size. In this particular case, the number of ground states is equal to half of the available spin configurations in any given row of the lattice.