Abelian Sandpile Model on the Honeycomb Lattice

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.

24 pages, 5 figures

References in corpus (4)

• 2D growth processes: SLE and Loewner chains
• The logarithmic triplet theory with boundary
• Pair correlations in sandpile model: a check of logarithmic conformal field theory
• Wind on the boundary for the Abelian sandpile model

Cited by in corpus (10)

• Abelian Manna model on various lattices in one and two dimensions
• Logarithmic conformal invariance in the Abelian sandpile model
• Logarithmic two-point correlators in the Abelian sandpile model
• Exact integration of height probabilities in the Abelian Sandpile Model
• Sandpile models in the large
• Cut-off for sandpiles on tiling graphs
• Sandpiles on the heptagonal tiling
• Sandpile probabilities on triangular and hexagonal lattices
• The spectrum of the abelian sandpile model
• General theory of perturbation of infinite resistor networks