Singularity spectrum of self-organized criticality

TL;DR

This paper presents a unified analytical framework using a Ginzburg-Landau based probability theory to relate self-organized criticality and multifractality, supported by numerical comparisons.

Contribution

It introduces a novel continuous probability model that analytically connects self-organized criticality with multifractal phenomena in condensed matter physics.

Findings

Analytical relation between self-organized criticality and multifractality.

Numerical validation with simulation data.

Identification of a nonlinear singularity spectrum distinct from typical multifractal measures.

Abstract

I introduce a simple continuous probability theory based on the Ginzburg-Landau equation that provides for the first time a common analytical basis to relate and describe the main features of two seemingly different phenomena of condensed-matter physics, namely self-organized criticality and multifractality. Numerical support is given by a comparison with reported simulation data. Within the theory the origin of self-organized critical phenomena is analysed in terms of a nonlinear singularity spectrum different from the typical convex shape due to multifractal measures.