Research Paper#Statistical Mechanics, Quasicrystals, Lattice-Gas Models🔬 ResearchAnalyzed: Jan 3, 2026 09:28
Quasicrystalline Gibbs States in 4D Lattice-Gas Models
Analysis
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.
Key Takeaways
- •Demonstrates the emergence of quasicrystalline order from finite-range interactions.
- •Utilizes the connection between probabilistic cellular automata and Gibbs measures.
- •Employs Ammann tiles and error-correction mechanisms for stability.
Reference
“The paper constructs a four-dimensional lattice-gas model with finite-range interactions that has non-periodic, ``quasicrystalline'' Gibbs states at low temperatures.”