  Order and disorder constitute two fundamental and opposite themes in
condensed matter physics and materials science. Crystals are considered the
epitome of order characterized by long-range translational order. The discovery
of quasicrystals, with no periodicity but rotational symmetries forbidden for
crystals, leads to a paradigm shift in solid-state physics. Moving one step
forward, it is intriguing to ask whether ordered matter exists without apparent
symmetry breaking. The same question may arise in the pursuit of how ordered
amorphous (noncrystalline) solids can be. Here we report the finding of ideal
noncrystals in two dimensions, which are disordered in the conventional sense
without Bragg peaks but highly ordered according to the steric order. We find
that such ideal noncrystals have vibrational modes the same as phonons
following the Debye law. The elastic responses are fully affine, which is again
characteristic of crystals, and the spatial fluctuations of local volume
fractions approach hyperuniformity. Therefore, ideal noncrystals represent an
anomalous form of matter with a mixed nature of noncrystalline structure but
crystal-like properties. Since such states are found to be thermodynamically
favorable, we identify them as a possible new class of ordered matter without
apparent broken symmetry. Our results thus extend the scope of the ordered
state of matter and may impact the understanding of entropy-driving ordering
also in generic amorphous materials.
