Absorbing-State Phase Transition for Driven-Dissipative Stochastic Dynamics on $Z$

TL;DR

This paper investigates the long-term behavior of certain driven-dissipative stochastic systems on the integer lattice, demonstrating that they exhibit an absorbing-state phase transition.

Contribution

It establishes the occurrence of an absorbing-state phase transition in both the activated random walk and stochastic sandpile models on Z.

Findings

Both models undergo an absorbing-state phase transition.

The results apply to reaction-diffusion systems and sandpile models.

Long-time behavior characterized by phase transition.

Abstract

We study the long-time behavior of conservative interacting particle systems in $Z$: the activated random walk model for reaction-diffusion systems and the stochastic sandpile. We prove that both systems undergo an absorbing-state phase transition.