Reply to "Comment on `Self-organized Criticality and Absorbing States: Lessons from the Ising Model'"

TL;DR

This paper discusses the conditions under which self-organized criticality arises in absorbing state models, emphasizing the dependence on dissipation and driving mechanisms, and clarifies previous findings on avalanche exponents.

Contribution

It clarifies the role of dissipation and external drive in self-organized criticality and responds to prior comments on avalanche exponents in absorbing state models.

Findings

Finite-size scaling depends on dissipation and driving implementation.

Avalanche exponent can become independent of dissipation and driving.

Clarifies the context of previous findings on avalanche exponents.

Abstract

In [Braz. J. Phys. 30, 27 (2000)] Dickman et al. suggested that self-organized criticality can be produced by coupling the activity of an absorbing state model to a dissipation mechanism and adding an external drive. We analyzed the proposed mechanism in [Phys. Rev. E 73, 025106R (2006)] and found that if this mechanism is at work, the finite-size scaling found in self-organized criticality will depend on the details of the implementation of dissipation and driving. In the preceding comment [Phys. Rev. E XX, XXXX (2008)] Alava et al. show that one avalanche exponent in the AS approach becomes independent of dissipation and driving. In our reply we clarify their findings and put them in the context of the original article.