  We explore the connection between self-organized criticality and phase
transitions in models with absorbing states. Sandpile models are found to
exhibit criticality only when a pair of relevant parameters - dissipation
epsilon and driving field h - are set to their critical values. The critical
values of epsilon and h are both equal to zero. The first is due to the absence
of saturation (no bound on energy) in the sandpile model, while the second
result is common to other absorbing-state transitions. The original definition
of the sandpile model places it at the point (epsilon=0, h=0+): it is critical
by definition. We argue power-law avalanche distributions are a general feature
of models with infinitely many absorbing configurations, when they are subject
to slow driving at the critical point. Our assertions are supported by
simulations of the sandpile at epsilon=h=0 and fixed energy density (no drive,
periodic boundaries), and of the slowly-driven pair contact process. We
formulate a field theory for the sandpile model, in which the order parameter
is coupled to a conserved energy density, which plays the role of an effective
creation rate.
