Finding ground states of a square Newman-Moore lattice with sides equal to a Mersenne number using the Rule 60 cellular automaton
arXiv:2407.19898 · doi:10.1080/17445760.2025.2531060
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.
17 pages, 0 figures. Submitted to Journal of Cellular Automata. Updated to correct typos and clarify language in abstract, introduction, and for several definitions and proofs. All results are unchanged