Pair correlations in sandpile model: a check of logarithmic conformal field theory

Abstract

We compute the correlations of two height variables in the two-dimensional Abelian sandpile model. We extend the known result for two minimal heights to the case when one of the heights is bigger than one. We find that the most dominant correlation log r/r^4 exactly fits the prediction obtained within the logarithmic conformal approach.

arXiv comment5 pages

References in corpus (20)

• Logarithmic Operators in Conformal Field Theory
• Bits and Pieces in Logarithmic Conformal Field Theory
• Indecomposable Fusion Products
• Polymers and percolation in two dimensions and twisted N=2 supersymmetry
• A Local Logarithmic Conformal Field Theory
• An algebraic approach to logarithmic conformal field theory
• Logarithmic Minimal Models
• Associative-algebraic approach to logarithmic conformal field theories
• 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
• Introduction to the Sandpile Model
• Logarithmic scaling for height variables in the Abelian sandpile model
• Correlation Functions of Dense Polymers and c=-2 Conformal Field Theory
• 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
• The four height variables, boundary correlations, and dissipative defects in the Abelian sandpile model
• Boundary conditions and defect lines in the Abelian sandpile model

Cited by in corpus (17)

• Size distributions of shocks and static avalanches from the Functional Renormalization Group
• Statistics of static avalanches in a random pinning landscape
• Integrable Boundary Conditions and W-Extended Fusion in the Logarithmic Minimal Models LM(1,p)
• Abelian Sandpile Model on the Honeycomb Lattice
• Logarithmic conformal invariance in the Abelian sandpile model
• Explicit characterization of the identity configuration in an Abelian Sandpile Model
• On logarithmic extensions of local scale-invariance
• Coset Graphs in Bulk and Boundary Logarithmic Minimal Models
• Logarithmic two-point correlators in the Abelian sandpile model
• Causality from dynamical symmetry: an example from local scale-invariance
• Two-dimensional spanning webs as (1,2) logarithmic minimal model
• Sandpile models in the large
• W-extended Kac representations and integrable boundary conditions in the logarithmic minimal models WLM(1,p)
• Three-leg correlations in the two component spanning tree on the upper half-plane
• Sandpile probabilities on triangular and hexagonal lattices
• Multipoint correlators in the Abelian sandpile model
• Watermelons on the half-plane