Hyperuniformity and the universal scaling of spectral densities of a generalized random organization model

The random organization model provides a means to produce hyperuniform state of matter at criticality. Previous studies focus on models based on monodisperse particles. We generalize the model to account for particle size disparity to investigate to what extent hyperuniformity can be preserved in such multicomponent systems. We begin with binary particles and find that the system is not multihyperuniform (each species is hyperuniform) at criticality but is hyperuniform as a two-phase medium. Specifically, the large-particle configuration is more ordered than the small-particle one. Moreover, when the particle size ratio tends to unity, the former becomes more disordered, while the later becomes more ordered. We show that the critical packing fraction shifts as the composition is varied, and so does the spectral density profile at the critical point. Interestingly, our simulations suggest that the spectral density profiles at the critical point can be rescaled to a single curve up to the first peak, implying a type of universal scaling of the large scale structures of these configurations. Finally, we extend our model to particles with a continuous size distribution. Our results suggest that random organization can be a robust way to produce hyperuniform multicomponent materials.