Avalanche and spreading exponents in systems with absorbing states

TL;DR

This paper derives universal scaling laws linking spreading and avalanche exponents in systems with absorbing states, providing a comprehensive collection of critical exponents across universality classes and highlighting potential non-universality in certain cases.

Contribution

It introduces generic scaling laws connecting different critical exponents and compiles state-of-the-art exponents for various universality classes, advancing understanding of self-organized criticality.

Findings

Scaling laws relate spreading and avalanche exponents.

Collection of critical exponents for directed and dynamical percolation.

Prediction of non-universality in avalanche exponents for systems with many absorbing states.

Abstract

We present generic scaling laws relating spreading critical exponents and avalanche exponents (in the sense of self-organized criticality) in general systems with absorbing states. Using these scaling laws we present a collection of the state-of-the-art exponents for directed percolation, dynamical percolation and other universality classes. This collection of results should help to elucidate the connections of self-organized criticality and systems with absorbing states. In particular, some non-universality in avalanche exponents is predicted for systems with many absorbing states.