Self-organized criticality and absorbing states: Lessons from the Ising model

We investigate a suggested path to self-organized criticality. Originally, this path was devised to "generate criticality" in systems displaying an absorbing-state phase transition, but nothing in its definition forbids the mechanism to be used in any other continuous phase transition. We used the Ising model as well as the Manna model to demonstrate how the finite-size scaling exponents depend on the tuning of driving and dissipation rates with system size. Our findings limit the explanatory power of the mechanism as it is to nonuniversal critical behavior, suggesting that the explanation of self-organized criticality in terms of absorbing-state phase transitions is incomplete.