Quasicrystal problem -- on rigidity of non-periodic structures from statistical mechanics point of view
Mathematical Physics
2024-12-30 v1 Statistical Mechanics
math.MP
Abstract
We present a brief history of quasicrystals and a short introduction to classical lattice-gas models of interacting particles. We discuss stability of non-periodic tilings and one-dimensional sequences of symbols seen as ground states of some hamiltonians. We argue that some sort of homogeneity, the so-called Strict Boundary Condition, is necessary for stability of non-periodic ground states against small perturbations of interactions and thermal fluctuations.
Keywords
Cite
@article{arxiv.2412.19594,
title = {Quasicrystal problem -- on rigidity of non-periodic structures from statistical mechanics point of view},
author = {Jacek Miȩkisz},
journal= {arXiv preprint arXiv:2412.19594},
year = {2024}
}
Comments
review paper, 13 pages, Proceedings of the XLI Workshop on Geometric Methods in Physics, Bia{\l}ystok, Poland, 1-6.07.2024