Distribution of Heights in the Abelian Sandpile Model on the Husimi Lattice

TL;DR

This paper derives exact expressions for the height distribution probabilities in the self-organized critical state of an Abelian sandpile model on a Husimi lattice with arbitrary coordination number q.

Contribution

It provides a novel analytical solution for height distributions in the Abelian sandpile model on Husimi lattices, extending understanding of self-organized criticality.

Findings

Exact height probability distributions derived for arbitrary q

Analytical expressions applicable to self-organized critical states

Enhanced understanding of sandpile dynamics on Husimi lattices

Abstract

An Abelian sandpile model is considered on the Husimi lattice of triangles with an arbitrary coordination number q. Exact expressions for the distribution of height probabilities in the Self-Organized Critical state are derived.