Quasicrystalline Gibbs States in 4D Lattice-Gas Models

This paper presents a novel construction of a 4-dimensional lattice-gas model exhibiting quasicrystalline Gibbs states. The significance lies in demonstrating the possibility of non-periodic order (quasicrystals) emerging from finite-range interactions, a fundamental question in statistical mechanics. The approach leverages the connection between probabilistic cellular automata and Gibbs measures, offering a unique perspective on the emergence of complex structures. The use of Ammann tiles and error-correction mechanisms is also noteworthy.