Onset of criticality and transport in a driven diffusive system

We study transport properties in a slowly driven diffusive system where the transport is externally controlled by a parameter $p$. Three types of behavior are found: For $p<p$ the system is not conducting at all. For intermediate $p$ a finite fraction of the external excitations propagate through the system. Third, in the regime $p>p_c$ the system becomes completely conducting. For all $p>p$ the system exhibits self-organized critical behavior. In the middle of this regime, at $p_c$, the system undergoes a continuous phase transition described by critical exponents.