Non-Abelian self-organized criticality model with one stochastic site in any avalanche shows multifractal scaling

TL;DR

This paper introduces a non-Abelian, stochastic self-organized criticality model with one stochastic site per avalanche, demonstrating multifractal scaling similar to Abelian models despite its non-Abelian and stochastic nature.

Contribution

It presents a novel non-Abelian, stochastic SOC model with a single stochastic site per avalanche, expanding understanding of multifractal scaling in such systems.

Findings

Avalanche structures exhibit shell-like formations.

Waves within avalanches are correlated.

Size moments and distributions show multifractal scaling.

Abstract

I have proposed a\textit{non-Abelian}and stochastic self-organized criticality model in which each avalanche contains one stochastic site and all remaining sites in the avalanche are deterministic with a constant threshold $E_{c}^{I}$. Studies of avalanche structures, waves and autocorrelations, size moments and probability distribution functions of avalanche size, for the thresholds $4\leq E_{c}^{I}\leq256$, were performed. The shell-like avalanche structures, correlated waves within avalanches, complex size moments and probability distribution functions show multifractal scaling like the \textit{Abelian} and deterministic BTW model despite the fact that the model is \textit{non-Abelian}and stochastic with unbalanced relaxation rules at each stochastic site.