Higher Dimensional Biased Random Organization

Random Organization (RO) and Biased Random Organization (BRO) models both exhibit dynamical phase transitions between absorbing and active states, in which active particles are displaced randomly in RO and displaced repulsively away from their overlapping neighbors in BRO. Both models have been dynamically and structurally characterized in detail in both 2D and 3D. RO in each case exhibits Manna universality class behavior; previous work has shown that 3D BRO remains Manna class, and approaches a random close packed (RCP) structure at a critical endpoint, while 2D BRO exhibits Manna behavior only above a certain displacement size and instead approaches a crystalline phase as displacement size approaches zero. Here, we extend the study of RO and BRO to higher dimensions and compare their behavior in 4D (the upper critical dimension for Manna class), including their critical exponents and hyperuniformity. Furthermore, we show that 4D BRO approaches the 4D RCP density calculated previously in literature.