Order Parameter and Scaling Fields in Self-Organized Criticality

TL;DR

This paper develops a unified mean-field theory for stochastic self-organized critical models, identifying key parameters and scaling fields, and validates the approach with numerical simulations, addressing inconsistencies in prior models.

Contribution

It introduces a single site approximation that incorporates model details via effective parameters, providing a consistent framework for analyzing critical behavior.

Findings

Identification of the order parameter and scaling fields.

Resolution of inconsistencies in previous mean-field approaches.

Numerical validation confirming the theory's accuracy.

Abstract

We present a unified dynamical mean-field theory for stochastic self-organized critical models. We use a single site approximation and we include the details of different models by using effective parameters and constraints. We identify the order parameter and the relevant scaling fields in order to describe the critical behavior in terms of usual concepts of non equilibrium lattice models with steady-states. We point out the inconsistencies of previous mean-field approaches, which lead to different predictions. Numerical simulations confirm the validity of our results beyond mean-field theory.