Random Close Packing is least random in 3D

Biased Random Organization (BRO) is a simple dynamical model that produces hyperuniform Random Close Packed (RCP) structures at its critical endpoint in 3D. BRO follows Manna universality class behavior, with an upper critical dimension of 4. We confirm mean field exponents for d≥4 through analysis of the fraction of active states and the distribution of interparticle gaps. Through simulations, we show that monodisperse BRO systems in d=3,4,5 recover RCP behavior at their critical endpoint with previously predicted packing fractions of φ=0.64, 0.45, and 0.30 respectively. Additionally, we find BRO in d=3,4,5 produces structures with their corresponding isostatic contact numbers Z=6, 8, and 10. While bidisperse BRO in 2D produces hyperuniform and isostatic critical states, the monodisperse case instead produces a crystalline state as its critical endpoint. This leads us to conjecture that BRO produces RCP as its critical endpoint in any dimension, suggesting that there is no RCP for monodisperse disks in 2D. Furthermore, we show that density fluctuations are random rather than hyperuniform in the mean field regime, S(q→0)~q⁰, leaving hyperuniformity to only be observed in 3D, S(q→0)~q^0.25.