A solvable non-conservative model of self-organised criticality

We present the first solvable non-conservative sandpile-like critical model of Self-Organised Criticality (SOC), and thereby substantiate the suggestion by Vespignani and Zapperi (Vespignani A. and Zapperi S., Phys. Rev. E, 57 (1998) 6345) that a lack of conservation in the microscopic dynamics of an SOC model can be compensated by introducing an external drive and thereby re-establishing criticality. The model shown is critical for all values of the conservation parameter. The analytical derivation follows the lines of Broker and Grassberger (Broker H.- M. and Grassberger P., Phys. Rev. E, 56 (1997) 3944) and is supported by numerical simulation. In the limit of vanishing conservation the Random Neighbour Drossel Schwabl Forest Fire Model (R-DS-FFM) is recovered.