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arXiv · 2412.19594

Quasicrystal problem -- on rigidity of non-periodic structures from statistical mechanics point of view

Jacek Miȩkisz
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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.

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Jacek Miȩkisz. 2024-12-27. Quasicrystal problem -- on rigidity of non-periodic structures from statistical mechanics point of view. https://arxiv.org/abs/2412.19594

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