Boundary conditions and defect lines in the Abelian sandpile model

Abstract

We add a defect line of dissipation, or crack, to the Abelian sandpile model. We find that the defect line renormalizes to separate the two-dimensional plane into two half planes with open boundary conditions. We also show that varying the amount of dissipation at a boundary of the Abelian sandpile model does not affect the universality class of the boundary condition. We demonstrate that a universal coefficient associated with height probabilities near the defect can be used to classify boundary conditions.

8 pages, 1 figure; suggestions from referees incorporated; to be published in Phys. Rev. E

References in corpus (6)

• Bits and Pieces in Logarithmic Conformal Field Theory
• Scaling fields in the two-dimensional abelian sandpile model
• A c=-2 boundary changing operator for the Abelian sandpile
• Modular transformation and boundary states in logarithmic conformal field theory
• Boundary States in c=-2 Logarithmic Conformal Field Theory
• Boundary states in boundary logarithmic CFT

Cited by in corpus (13)

• Height variables in the Abelian sandpile model: scaling fields and correlations
• Logarithmic scaling for height variables in the Abelian sandpile model
• Abelian Sandpile Model: a Conformal Field Theory Point of View
• Pre-logarithmic and logarithmic fields in a sandpile model
• Pair correlations in sandpile model: a check of logarithmic conformal field theory
• The four height variables, boundary correlations, and dissipative defects in the Abelian sandpile model
• Wind on the boundary for the Abelian sandpile model
• Logarithmic two-point correlators in the Abelian sandpile model
• Three-leg correlations in the two component spanning tree on the upper half-plane
• The four height variables of the Abelian sandpile model
• Sandpile probabilities on triangular and hexagonal lattices
• Higher Order and boundary Scaling Fields in the Abelian Sandpile Model
• Spatial Asymmetric Two dimensional Continuous Abelian Sandpile Model