Cloaking the underlying long-range order of randomly perturbed lattices

Abstract

Random, uncorrelated displacements of particles on a lattice preserve the hyperuniformity of the original lattice, that is, normalized density fluctuations vanish in the limit of infinite wavelengths. In addition to a diffuse contribution, the scattering intensity from the the resulting point pattern typically inherits the Bragg peaks (long-range order) of the original lattice. Here we demonstrate how these Bragg peaks can be hidden in the effective diffraction pattern of independent and identically distributed perturbations. All Bragg peaks vanish if and only if the sum of all probability densities of the positions of the shifted lattice points is a constant at all positions. The underlying longrange order is then 'cloaked' in the sense that it cannot be reconstructed from the pair correlation function alone. On the one hand, density fluctuations increase monotonically with the strength of perturbations a, as measured by the hyperuniformity order metric Λ. On the other hand, the disappearance and reemergence of long-range order, depending on whether the system is cloaked or not as the perturbation strength increases, is manifestly captured by the τ order metric. Therefore, while the perturbation strength a may seem to be a natural choice for an order metric of perturbed lattices, the τ order metric is a superior choice. It is noteworthy that cloaked perturbed lattices allow one to easily simulate very large samples (with at least 10 6 particles) of disordered hyperuniform point patterns without Bragg peaks.

Stone–Wales defects preserve hyperuniformity in amorphous two-dimensional networks

“…In addition, we note that in this work we discovered a hyperuniformity-preserving operation in two dimensions: SW transformation. Previously, it was found that operations such as "uncorrelated" stochastic displacements in perfect lattices preserve hyperuniformity but could change the hyperuniformity class of the systems (40,42,43), similar to what we observed in this work. Moreover, hyperuniformity-generating operations that can convert nonhyperuniform point patterns into hyperuniform materials have also been discovered (28,69).…”

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“…Further work in this direction is certainly needed. Future investigations may also consider the possibility of artificially tuning the Gaussian behavior through local particle displacements [34].…”

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