Non-equilibrium Phase Transitions: Activated Random Walks at Criticality

Abstract

In this paper we present rigorous results on the critical behavior of the Activated Random Walk model. We conjecture that on a general class of graphs, including Z d , and under general initial conditions, the system at the critical point does not reach an absorbing state. We prove this for the case where the sleep rate λ is infinite. Moreover, for the one-dimensional asymmetric system, we identify the scaling limit of the flow through the origin at criticality. The case λ < +∞ remains largely open, with the exception of the one-dimensional totally-asymmetric case, for which it is known that there is no fixation at criticality.