A many-particle system in d -dimensional Euclidean space R d is said to be hyperuniform if the number of points in a spherical observation window with radius R has a variance σ σ N 2 ( R ) that scales slower than the volume of the observation window: lim R → → ∞ ∞ σ σ N 2 ( R ) R d = 0. This definition is (essentially) equivalent to the vanishing of the structure factor at the origin: lim k → → 0 S ( k ) = 0 for wave vectors k ∈ ∈ R d .