Self-organised criticality in stochastic sandpiles: Connection to directed percolation

We introduce a stochastic sandpile model where finite drive and dissipation are coupled to the activity field. The absorbing phase transition here, as expected, belongs to the directed percolation (DP) universality class. We focus on the small drive and dissipation limit, i.e. the so-called self-organised critical (SOC) regime and show that the system exhibits a crossover from ordinary DP scaling to a dissipation-controlled scaling which is independent of the underlying dynamics or spatial dimension. The new scaling regime continues all the way to the zero bulk drive limit suggesting that the corresponding SOC behaviour is only DP, modified by the dissipation-controlled scaling. We demonstrate this for the continuous and discrete Manna model driven by noise and bulk dissipation.