Contact processes in crowded environments

Abstract

Periodically sheared colloids at low densities demonstrate a dynamical phase transition from an inactive to active phase as the strain amplitude is increased. The inactive phase consists of no collisions (contacts) between particles in the steady state limit, while in the active phase collisions persist. To investigate this system at higher densities, we construct and study a conserved-particle-number contact process with three-body interactions, which are potentially more likely than two-body interactions at higher densities. For example, consider one active (diffusing) particle colliding with two inactive (nondiffusing) particles such that they become active and consider spontaneous inactivation. In mean field, this system exhibits a continuous dynamical phase transition. Simulations on square lattices also indicate a continuous transition with exponents similar to those measured for the conserved lattice gas (CLG) model. In contrast, the three-body interaction requiring two active particles to activate one inactive particle exhibits a discontinuous transition. Finally, inspired by kinetically constrained models of the glass transition, we investigate the "caging effect" at even higher particle densities to look for a second dynamical phase transition back to an inactive phase. Square lattice simulations suggest a continuous transition with a new set of exponents differing from both the CLG model and what is known as directed percolation, indicating a potentially new universality class for a contact process with a conserved particle number.