Conserved dynamics make the solute hyperuniform, not the domains

Abstract

Analysis code, derived data and manuscript source for a study of spatial order in Cahn–Hilliard coarsening. In a phase-separating system with a locally conserved order parameter, the concentration field is hyperuniform, with Sc(k) ~ k⁴, while the point pattern of domain centroids is not: S(k→0) settles on a plateau near 0.14 and the number variance grows with window area rather than perimeter. Weighting the same points by domain solute mass restores hyperuniformity, S(k→0) = 0.021. A variance budget built on a parameter-free identity shows the measured solute-mass fluctuation to be a factor of eight below what independent domains of the observed size distribution would produce, with the shortfall supplied by an anticorrelation between domain count and mean domain size that deepens monotonically with window size. Contents: the simulation and point-pattern pipeline (structure factor evaluated on the exact reciprocal lattice of the periodic box, number variance, Clark–Evans index, and matched complete-spatial-random, hard-core and perturbed-lattice nulls); the mass-autocorrelation and mark-permutation analysis; derived per-field statistics for 1024² and 512² ensembles; a per-domain table of 10,942 domains with centroid coordinates, area and solute mass, from which every reported budget quantity can be recomputed without repeating the simulations; the journal figures; and the manuscript source. Estimators are validated in every run by passing a complete-spatial-random null through the identical pipeline, which returns R = 0.99, S(k→0) = 1.14 and a number-variance slope of 2.02, against the ideal values of 1, 1 and 2.