A Nearest-Neighbor Hard-Core Model on a Penrose Graph
Mathematical Physics
2026-04-24 v1 math.MP
Probability
Abstract
We prove that the maximal graph-density of an independent set in a Penrose P3 tiling considered as a planar non-directed graph is equal to despite the fact that the graph is bipartite. Accordingly, the extreme Gibbs measure of the nearest-neighbor hard core particle model on this graph is unique for sufficiently large values of the particle activity. This invalidates a natural expectation to observe the coexistence of even and odd phases.
Cite
@article{arxiv.2604.21086,
title = {A Nearest-Neighbor Hard-Core Model on a Penrose Graph},
author = {A. Mazel and I. Stuhl and Y. Suhov},
journal= {arXiv preprint arXiv:2604.21086},
year = {2026}
}