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<p>Order and disorder are central concepts in condensed-matter physics. Crystals break translational and rotational symmetries, whereas quasicrystals challenge this paradigm with forbidden rotational symmetries and aperiodicity. Here we report a distinct ordered state—ideal non-crystals—characterized by optimal steric order without symmetry breaking. Steric optimization yields ideal non-crystals as a thermodynamically favoured limiting state, accompanied by maximal steric order that may serve as a true order parameter for the glass transition. Despite their apparent disorder, they exhibit long-range orientational correlations, quantified via a specific path-integral-like approach. Ideal non-crystals possess distinct properties, including Debye-like phononic modes, affine elasticity, thermodynamic ultrastability and long-wavelength density uniformity, reminiscent of hyperuniformity. By uncovering a distinct form of entropy-driven ordering in sterically optimized materials, this work expands the landscape of ordered states and provides a framework for designing amorphous materials with crystal-like mechanical and thermal properties free from the anisotropy inherent in crystals.</p>

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Ideal non-crystals as a distinct form of ordered states without symmetry breaking

  • 期刊论文

  • 发表日期：

    2026年2月13日

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  • Xinyu Fan,
  • Ding Xu,
  • Jianhua Zhang,
  • Hao Hu,
  • Peng Tan,
  • Ning Xu,
  • Hajime Tanaka,
  • Hua Tong

摘要

Order and disorder are central concepts in condensed-matter physics. Crystals break translational and rotational symmetries, whereas quasicrystals challenge this paradigm with forbidden rotational symmetries and aperiodicity. Here we report a distinct ordered state—ideal non-crystals—characterized by optimal steric order without symmetry breaking. Steric optimization yields ideal non-crystals as a thermodynamically favoured limiting state, accompanied by maximal steric order that may serve as a true order parameter for the glass transition. Despite their apparent disorder, they exhibit long-range orientational correlations, quantified via a specific path-integral-like approach. Ideal non-crystals possess distinct properties, including Debye-like phononic modes, affine elasticity, thermodynamic ultrastability and long-wavelength density uniformity, reminiscent of hyperuniformity. By uncovering a distinct form of entropy-driven ordering in sterically optimized materials, this work expands the landscape of ordered states and provides a framework for designing amorphous materials with crystal-like mechanical and thermal properties free from the anisotropy inherent in crystals.