Hyperuniformity and absorbing phase transition in continuous media with a conserved field

The nonequilibrium absorbing phase transition of interacting particles in two-dimensional continuous media is investigated via Monte Carlo simulations. Starting from random and natural homogeneous distributions of equi-sized spherical particles (disks) in an off-lattice continuous medium, particles that overlap with other particles are considered to be active and isolated particles are considered inactive. Active particles tend to repel overlapping particles. In a steady state, the particle distribution is found to be hyperuniform with a larger hyperuniformity exponent than the lattice Manna model. The critical exponents that characterize the power laws of the steady-state densities and the critical active-particle densities are calculated using both the sequential and parallel updates; they are found to be consistent, within the statistical margin of error, with those of the lattice Manna model but are distinctly different from those of the directed percolation universality class. The influence of impurities is also investigated by adding quenched point-impurity particles, and it is found that the impurity has a negligible effect on the critical behavior, supporting the universality between the continuum model and lattice Manna model. The results are in disagreement with the recent observations.