Quasicrystalline Gibbs states in 4-dimensional lattice-gas models with finite-range interactions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917177787940864 |
|---|---|
| author | Taati, Siamak Miȩkisz, Jacek |
| author_facet | Taati, Siamak Miȩkisz, Jacek |
| contents | We construct a four-dimensional lattice-gas model with finite-range interactions that has non-periodic, ``quasicrystalline'' Gibbs states at low temperatures. Such Gibbs states are probability measures which are small perturbations of non-periodic ground-state configurations corresponding to tilings of the plane with Ammann's aperiodic tiles. Our construction is based on the correspondence between probabilistic cellular automata and Gibbs measures on their space-time trajectories, and a classical result on noise-resilient computing with cellular automata. The cellular automaton is constructed on the basis of Ammann's tiles, which are deterministic in one direction, and has non-periodic space-time trajectories corresponding to each valid tiling. Repetitions along two extra dimensions, together with an error-correction mechanism, ensure stability of the trajectories subjected to noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24436 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasicrystalline Gibbs states in 4-dimensional lattice-gas models with finite-range interactions Taati, Siamak Miȩkisz, Jacek Mathematical Physics Statistical Mechanics Discrete Mathematics Probability Cellular Automata and Lattice Gases We construct a four-dimensional lattice-gas model with finite-range interactions that has non-periodic, ``quasicrystalline'' Gibbs states at low temperatures. Such Gibbs states are probability measures which are small perturbations of non-periodic ground-state configurations corresponding to tilings of the plane with Ammann's aperiodic tiles. Our construction is based on the correspondence between probabilistic cellular automata and Gibbs measures on their space-time trajectories, and a classical result on noise-resilient computing with cellular automata. The cellular automaton is constructed on the basis of Ammann's tiles, which are deterministic in one direction, and has non-periodic space-time trajectories corresponding to each valid tiling. Repetitions along two extra dimensions, together with an error-correction mechanism, ensure stability of the trajectories subjected to noise. |
| title | Quasicrystalline Gibbs states in 4-dimensional lattice-gas models with finite-range interactions |
| topic | Mathematical Physics Statistical Mechanics Discrete Mathematics Probability Cellular Automata and Lattice Gases |
| url | https://arxiv.org/abs/2512.24436 |