Self-Organizing Height-Arrow Model: Numerical and Analytical Results

TL;DR

This paper investigates the self-organizing height-arrow (HA) model through numerical and analytical methods, revealing its critical behavior and universality class similarity to the BTW model on square and Bethe lattices.

Contribution

It provides the first detailed numerical and analytical analysis of the HA model, including critical exponents and occupied site concentration, establishing its relation to the BTW model.

Findings

Critical exponents close to BTW model

Occupied site concentration calculated exactly on Bethe lattice

HA model belongs to the same universality class as BTW

Abstract

The recently introduced self-organizing height-arrow (HA) model is numerically investigated on the square lattice and analytically on the Bethe lattice. The concentration of occupied sites and critical exponents of distributions of avalanches are evaluated for two slightly different versions of the model. The obtained exponents for distributions of avalanches by mass, area, duration and appropriate fractal dimensions are close to those for the BTW model, which suggests that the HA model belongs to the same universality class. For comparison, the concentration of occupied sites in the HA model is calculated exactly on the Bethe lattice of coordination number $q=4$ as well.