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 (24)

• Application of the lattice Green's function for calculating the resistance of an infinite networks of resistors
• The dimension of the SLE curves
• 2D growth processes: SLE and Loewner chains
• Conformal Field Theories of Stochastic Loewner Evolutions
• Spanning Trees on Graphs and Lattices in d Dimensions
• Inverse turbulent cascades and conformally invariant curves
• Curiosities at c=-2
• Scaling fields in the two-dimensional abelian sandpile model
• Height variables in the Abelian sandpile model: scaling fields and correlations
• A c=-2 boundary changing operator for the Abelian sandpile
• The logarithmic triplet theory with boundary
• Logarithmic scaling for height variables in the Abelian sandpile model
• Abelian Sandpile Model: a Conformal Field Theory Point of View
• Boundary height fields in the Abelian sandpile model
• Pre-logarithmic and logarithmic fields in a sandpile model
• Conformal field theory correlations in the Abelian sandpile mode
• Pair correlations in sandpile model: a check of logarithmic conformal field theory
• Direct Evidence for Conformal Invariance of Avalanche Frontier in Sandpile Models
• The four height variables, boundary correlations, and dissipative defects in the Abelian sandpile model
• Wind on the boundary for the Abelian sandpile model
• Expansion and Contraction of Avalanches in 2D Abelian Sandpile
• Renormalization group approach to an Abelian sandpile model on planar lattices
• Renormalization Group Study of Sandpile on the Triangular Lattice
• Geometrical Properties of Loops and Cluster Boundaries

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