Self-organized Criticality and Absorbing States: Lessons from the Ising Model

TL;DR

This paper explores the connection between self-organized criticality and absorbing states using the Ising and Manna models, revealing limitations in the mechanism's ability to explain universal critical phenomena.

Contribution

It demonstrates that the mechanism for self-organized criticality is limited to non-universal critical behavior and depends on specific tuning of system parameters.

Findings

Finite-size scaling exponents depend on driving and dissipation rates.

The mechanism explains only non-universal critical behavior.

Self-organized criticality does not generically produce universal criticality.

Abstract

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 closer examination of the mechanism reveals that it can be used for any 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 to non-universal critical behavior.