Self-Organized Criticality on Quasiperiodic Graphs

TL;DR

This paper investigates self-organized criticality on quasiperiodic graphs, comparing its behavior to traditional periodic lattices, and explores how graph structure influences critical phenomena in SOC models.

Contribution

It introduces the implementation of SOC models on quasiperiodic graphs and analyzes their properties relative to standard periodic lattices.

Findings

SOC behavior varies with graph isotropy and anisotropy.

Quasiperiodic graphs exhibit distinct critical properties from square lattices.

Comparison highlights the influence of underlying graph topology on SOC dynamics.

Abstract

Self-organized critical models are used to describe the 1/f-spectra of rather different physical situations like snow avalanches, noise of electric currents, luminosities of stars or topologies of landscapes. The prototype of the SOC-models is the sandpile model of Bak, Tang and Wiesenfeld (Phys. Rev. Lett. 59, (1987) 351). We implement this model on non-periodic graphs where it can become either isotropic or anisotropic and compare its properties with the periodic counterpart on the square lattice.