Rule 60 cellular automaton, Mersenne numbers, and the Newman-Moore spin lattice

The goal of this paper is to review the properties of a Rule 60 cellular automaton on a ring with a Mersenne number circumference and to use this knowledge to explicitly construct all the ground state configurations of the classical Newman-Moore model (a particular two-dimensional spin lattice model...

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Bibliographic Details
Published in:arXiv.org 2024-07
Main Authors: Carmona-Pírez, Jonás, Peguero, Adrian J, Dunjko, Vanja, Olshanii, Maxim, Ruhl, Joanna
Format: Article
Language:English
Subjects:
Cellular automata
Configurations
Ground state
Prime numbers
Online Access:Get full text
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Summary:The goal of this paper is to review the properties of a Rule 60 cellular automaton on a ring with a Mersenne number circumference and to use this knowledge to explicitly construct all the ground state configurations of the classical Newman-Moore model (a particular two-dimensional spin lattice model with a specific three-spin interaction) 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.
ISSN:2331-8422