Beyond the freshman's dream: Classical fractal spin liquids from matrix cellular automata in three-dimensional lattice models

The Newman-Moore model on the 2D triangular lattice is a classic example of a statistical mechanical model with immobile fractal excitations: fractons. These result in kinetic constraints leading to glassy behavior. Here, the authors generalize this construction to two 3D lattices, trillium and hyperhyperkagome. While these models exhibit a similar phenomenology, the authors show that the underlying fractons have a richer structure and are intimately connected to the matrix cellular automata that describe the manifold of ground states.