• Abstract 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.
Article Summaries:
- A new study introduces “ideal non‑crystals,” a class of ordered states that achieve maximal steric order without breaking translational or rotational symmetry. Unlike conventional crystals, these structures lack long‑range positional order but exhibit long‑range orientational correlations, quantified by a path‑integral‑like metric. The authors show that steric optimization drives these states to a thermodynamically favored limit, yielding Debye‑like phonons, affine elasticity, and hyperuniform‑like density uniformity. They propose that the resulting long‑range orientational order could serve as an order parameter for the glass transition. The work expands the taxonomy of ordered matter and offers a framework for designing amorphous materials with crystal‑like mechanical and thermal properties.
Sources: