  We consider Activated Random Walk (ARW), a model which generalizes the
Stochastic Sandpile, one of the canonical examples of self organized
criticality. Informally ARW is a particle system on $\mathbb{Z}$ with mass
conservation. One starts with a mass density $\mu>0$ of initially active
particles, each of which performs a symmetric random walk at rate one and falls
asleep at rate $\lambda>0$. Sleepy particles become active on coming in contact
with other active particles. We investigate the question of
fixation/non-fixation of the process, and show for small enough $\lambda$, the
critical mass density for fixation is strictly less than one. Moreover, the
critical density goes to zero as $\lambda$ tends to zero. This settles a long
standing open question.
