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We present a brief history of quasicrystals and a short introduction to classical lattice-gas models of interacting particles. We discuss stability of nonperiodic 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 nonperiodic ground states against small perturbations of interactions and thermal fluctuations.

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Quasicrystal Problem—on Rigidity of Nonperiodic Structures from Statistical Mechanics Point of View

  • 会议论文

  • 发表日期：

    2025年

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  • Jacek Miękisz

摘要

We present a brief history of quasicrystals and a short introduction to classical lattice-gas models of interacting particles. We discuss stability of nonperiodic 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 nonperiodic ground states against small perturbations of interactions and thermal fluctuations.