Abelian Sandpile Model on the Husimi Lattice of Square Plaquettes

TL;DR

This paper analyzes the Abelian sandpile model on a Husimi lattice of squares, deriving exact height distributions and correlation functions in the self-organized critical state, advancing understanding of critical phenomena on complex lattices.

Contribution

It provides exact analytical expressions for height probabilities and correlations in the Abelian sandpile model on the Husimi lattice, a novel lattice structure.

Findings

Exact height probability distributions in the SOC state

Exact two-point correlation functions deep inside the lattice

Analytical results for critical behavior on Husimi lattice

Abstract

An Abelian sandpile model is considered on the Husimi lattice of square plaquettes. Exact expressions for the distribution of height probabilities in the Self-Organized Critical state are derived. The two-point correlation function for the sites deep inside the Husimi lattice is calculated exactly.