Hyperuniformity in ideal noncrystals at vanishing steric disorder

Verify whether two-dimensional ideal noncrystals exhibit class I hyperuniformity in the low-wavenumber limit as the steric order parameter Θ→0, specifically establishing a power-law spectral density χV(k)∼kα for k→0 (e.g., χV(k)∼k3) and determining the existence of the power-law regime for k<1.

Background

Approaching INC, the spectral density χV(k) displays behavior reminiscent of class I hyperuniformity, though imperfections induce a plateau at the lowest k. The authors observe a scaling of the plateau with the steric order parameter Θ, suggesting underlying hyperuniformity as Θ→0.

They state that the low-k power-law regime (k<1) is not observed in their data and explicitly call for further investigation to verify their conjecture of hyperuniformity in the ideal limit.