Abelian Sandpile Model on the Honeycomb Lattice

TL;DR

This paper investigates the Abelian sandpile model on a honeycomb lattice, deriving exact correlation functions and analyzing avalanche boundaries using SLE theory, suggesting conformal invariance.

Contribution

It provides the first detailed analysis of the Abelian sandpile model on a honeycomb lattice, including exact correlation functions and boundary statistics.

Findings

Correlation functions derived for honeycomb lattice

Avalanche boundaries exhibit conformal invariance

Boundaries are described by SLE2

Abstract

We check the universality properties of the two-dimensional Abelian sandpile model by computing some of its properties on the honeycomb lattice. Exact expressions for unit height correlation functions in presence of boundaries and for different boundary conditions are derived. Also, we study the statistics of the boundaries of avalanche waves by using the theory of SLE and suggest that these curves are conformally invariant and described by SLE2.