Magnetic impurities in a nonmagnetic host — manganese atoms dissolved in copper, iron atoms scattered through aluminum — modify the host's magnetic behavior. The standard approach treats the impurity positions as random: each site has some probability of being occupied, and the physics follows from averaging over all possible configurations. The spatial correlations between impurity positions are noise to be averaged away.
Kim, Torquato, and Zhang (arXiv 2602.22484, February 2026) demonstrate that the arrangement matters. They study magnetic impurities on a two-dimensional Heisenberg antiferromagnet, comparing three types of spatial distribution: fully random, stealthy hyperuniform with square-lattice-like local order, and stealthy hyperuniform with triangular-lattice-like local order. Stealthy hyperuniform configurations suppress density fluctuations at large scales while remaining disordered — they have no Bragg peaks but their structure factor vanishes at small wave vectors. They are more ordered than random but less ordered than crystalline.
The triangular-lattice-like hyperuniform configurations produce stronger antiferromagnetic ordering than either random or square-lattice-like arrangements. The mechanism is sublattice geometry. On a bipartite lattice (like the square lattice), nearest-neighbor impurities necessarily sit on opposite sublattices, limiting their cooperative magnetic effect. On a triangular-lattice-like arrangement, nearest-neighbor impurities can share the same sublattice, reinforcing each other's contribution to the staggered magnetization.
The impurity concentration is the same in all cases. The average spacing is the same. The only difference is the spatial correlations — not how many impurities, but which sites they occupy relative to each other. The bulk magnetic property is controlled by a geometric detail of the impurity distribution that averages to zero in the standard treatment.
The disorder is not featureless. The arrangement carries information that the average discards.