Scaling fields in the two-dimensional Abelian sandpile model.

We consider the unoriented two-dimensional Abelian sandpile model from a perspective based on two-dimensional (conformal) field theory. We compute lattice correlation functions for various cluster variables (at and off criticality), from which we infer the field-theoretic description in the scaling limit. We find perfect agreement with the predictions of a c=-2 conformal field theory and its massive perturbation, thereby providing direct evidence for conformal invariance and more generally for a description in terms of a local field theory. The question of the height 2 variable is also addressed, with, however, no definite conclusion yet.

• Publication year

  2001

• Venue

  Physical review. E, Statistical, nonlinear, and soft matter physics

• Publication date

  2001-07-18

• Fields of study

  Medicine, Physics, Mathematics

• Identifiers
  DOI 10.1103/PhysRevE.64.066130arXiv hep-th/0107150PMID 11736259
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Proof of breaking of self-organized criticality in a nonconservative abelian sandpile model

  2000cited by this paper
• Nonconservative abelian sandpile model with the bak-tang-wiesenfeld toppling rule

  2000cited by this paper
• Studying Self-Organized Criticality with Exactly Solved Models

  1999cited by this paper
• Fractals and Chaos in Geology and Geophysics: Self-organized criticality

  1997cited by this paper
• How Nature Works: The Science of Self-Organized Criticality

  1997cited by this paper
• Curiosities at c=-2

  1995cited by this paper
• Self-organized critical state of sandpile automaton models.

  1990cited by this paper
• An Atlas of Functions.

  1988cited by this paper
• Self-organized criticality: An explanation of the 1/f noise.

  1987cited by this paper
• The Two-Dimensional Ising Model

  1973cited by this paper
• Principles Of Random Walk

  1965cited by this paper

• Dynamic Balance: A Thermodynamic Principle for the Emergence of the Golden Ratio in Open Non-Equilibrium Steady States

  2025cites this paper
• Vibrating sandpiles: An example of systems with directionality transition.

  2025cites this paper
• Topological data analysis of the visibility graphs of the BTW avalanche-size sequences

  2024cites this paper
• Symplectic fermions in general domains

  2024cites this paper
• Lattice Models and Conformal Field Theory

  2024cites this paper
• Fermionic Gaussian free field structure in the Abelian sandpile model and uniform spanning tree

  2023cites this paper
• Taming obstinate spreaders: the dynamics of a rumor spreading model incorporating inhibiting mechanisms and attitude adjustment

  2021cites this paper
• Sandpile Models in the Large

  2021influential citation
• Some properties of sandpile models as prototype of self-organized critical systems

  2020cites this paper
• Self-organized criticality in cumulus clouds.

  2020cites this paper
• The stochastic evolution of a rumor spreading model with two distinct spread inhibiting and attitude adjusting mechanisms in a homogeneous social network

  2020cites this paper
• Analytic bootstrap for logarithmic CFT

  2019cites this paper
• Dynamic behavior of an I2S2R rumor propagation model on weighted contract networks

  2019cites this paper
• Coupling of c  =  −2 and c =12 and c  =  0 conformal field theories: the geometrical point of view

  2018cites this paper
• Multipoint correlators in the Abelian sandpile model

  2017cites this paper
• Sandpile probabilities on triangular and hexagonal lattices

  2017cites this paper
• Mapping of the Bak, Tang, and Wiesenfeld sandpile model on a two-dimensional Ising-correlated percolation lattice to the two-dimensional self-avoiding random walk.

  2017cites this paper
• Bak-Tang-Wiesenfeld model in the upper critical dimension: Induced criticality in lower-dimensional subsystems.

  2017cites this paper
• Spatio-temporal Correlations in the Manna Model in one, three and five dimensions

  2016cites this paper
• Complex dynamic behavior of a rumor propagation model with spatial-temporal diffusion terms

  2016cites this paper
• Fundamental constants in the theory of two-dimensional uniform spanning trees

  2016cites this paper
• Fundamental constants in the theory of two-dimensional uniform spanning trees

  2016cites this paper
• Dissipative Abelian Sandpile Models

  2015cites this paper
• Statistical investigation of the cross sections of wave clusters in the three-dimensional Bak-Tang-Wiesenfeld model.

  2015cites this paper
• Frontal cellular automata for the study of non-equilibrium lattice models

  2015cites this paper
• Continuous transforming the BTW to the Manna model

  2015cites this paper
• The effect of the number of dissipative sites on a sandpile model

  2015cites this paper
• Approaching Criticality via the Zero Dissipation Limit in the Abelian Avalanche Model

  2015influential citation
• Annealed and quenched disorder in sand-pile models with local violation of conservation.

  2015cites this paper
• Predictions and Correlations in Self-Organised Criticality

  2015cites this paper
• Logarithmic violation of scaling in strongly anisotropic turbulent transfer of a passive vector field.

  2014cites this paper
• Green's function on lattices

  2014cites this paper
• Holographic applications of logarithmic conformal field theories

  2013cites this paper
• Logarithmic conformal invariance in the Abelian sandpile model

  2013influential citation
• Logarithmic correlators or responses in non-relativistic analogues of conformal invariance

  2013cites this paper
• Amplitude ratios for critical systems in the c=-2 universality class.

  2013cites this paper
• Bak–Tang–Wiesenfeld model in the finite range random link lattice

  2013cites this paper
• Statistics of toppling wave boundaries in deterministic and stochastic sandpile models

  2012cites this paper
• Minimal Configurations and Sandpile Measures

  2012cites this paper
• Discrete Holomorphic Parafermions in the Eight Vertex Model

  2012cites this paper
• Avalanche frontiers in the dissipative Abelian sandpile model and off-critical Schramm-Loewner evolution.

  2012cites this paper
• Numerical determination of the boundary condition changing operators

  2012cites this paper
• Observation of SLE(κ, ρ) on the critical statistical models

  2011cites this paper
• Indecomposability parameters in chiral logarithmic conformal field theory

  2011cites this paper
• Minimal Configurations and Sandpile Measures

  2011cites this paper
• Return probability for the loop-erased random walk and mean height in the Abelian sandpile model: a proof

  2011cites this paper
• -extended Kac representations and integrable boundary conditions in the logarithmic minimal models

  2011cites this paper
• Multiple and inverse topplings in the Abelian Sandpile Model

  2011cites this paper
• Logarithmic correlators in nonrelativistic conformal field theory

  2010cites this paper
• Logarithmic two-point correlators in the Abelian sandpile model

  2010cites this paper
• Coset graphs in bulk and boundary logarithmic minimal models

  2010cites this paper
• Zero dissipation limit in the Abelian sandpile model

  2009cites this paper
• Patterned and disordered continuous Abelian sandpile model.

  2009cites this paper
• The Baxter Q operator of critical dense polymers

  2009cites this paper
• Approaching Criticality via the Zero Dissipation Limit in the Abelian Avalanche Model

  2009cites this paper
• The Abelian sandpile model on the honeycomb lattice

  2009cites this paper
• Three-leg correlations in the two-component spanning tree on the upper half-plane

  2009cites this paper
• Conformal covariance of the Abelian sandpile height one field

  2009cites this paper
• Integrals of motion for critical dense polymers and symplectic fermions

  2009cites this paper
• The spatial asymmetric two-dimensional continuous Abelian sandpile model

  2008cites this paper
• Explicit characterization of the identity configuration in an Abelian sandpile model

  2008cites this paper
• Direct evidence for conformal invariance of avalanche frontiers in sandpile models.

  2008cites this paper
• A pr 2 00 2 Logarithmic conformal field theory with boundary †

  2008cites this paper
• Pair correlations in sandpile model: A Check of logarithmic conformal field theory

  2007cites this paper
• Wind on the boundary for the Abelian sandpile model

  2007cites this paper
• Continuous Abelian Sandpile Model in Two Dimensional Lattice

  2007cites this paper
• Higher order and boundary scaling fields in the Abelian sandpile model

  2006cites this paper
• Solvable critical dense polymers

  2006cites this paper
• Course 14 – Mathematical Aspects of the Abelian Sandpile Model

  2006cites this paper
• Some aspects of c = ‐2 theory

  2006cites this paper
• Indecomposable representations in Zn symmetric b, c ghost systems via deformations of the Virasoro field

  2006cites this paper
• Height variables in the Abelian sandpile model: scaling fields and correlations

  2006cites this paper
• Dynamical invariants in the deterministic fixed-energy sandpile

  2005cites this paper
• Mathematical aspects of the abelian sandpile models

  2005cites this paper
• Mathematical aspects of the abelian sandpile model

  2005cites this paper
• Four-point functions in logarithmic conformal field theories

  2005cites this paper
• Perturbed Logarithmic CFT and Integrable Models

  2005cites this paper
• Conformal field theory correlations in the Abelian sandpile model.

  2004cites this paper
• Four height variables, boundary correlations, and dissipative defects in the Abelian sandpile model.

  2004cites this paper
• Boundary height fields in the Abelian sandpile model

  2004cites this paper
• Logarithmic scaling for height variables in the Abelian sandpile model

  2004cites this paper
• Abelian Sandpile Model: a Conformal Field Theory Point of View

  2004cites this paper
• Pre-logarithmic and logarithmic fields in a sandpile model

  2004cites this paper
• Infinite Volume Limit for the Stationary Distribution of Abelian Sandpile Models

  2004cites this paper
• The Raise and Peel Model of a Fluctuating Interface

  2003cites this paper
• Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas

  2003cites this paper
• Boundary conditions and defect lines in the Abelian sandpile model.

  2003cites this paper
• Logarithmic conformal field theory with boundary

  2002cites this paper
• Extended multiplet structure in Logarithmic Conformal Field Theories

  2002cites this paper
• A c=-2 boundary changing operator for the Abelian sandpile model

  2002cites this paper
• The Infinite Volume Limit of Dissipative Abelian Sandpiles

  2002cites this paper
• Boundary States in Logarithmic Conformal Field Theory — A novel Approach —

  2002cites this paper
• 2 2 1 M ar 2 00 2 Operator Product Expansion in Logarithmic Conformal Field Theory

  2002cites this paper
• Bits and Pieces in Logarithmic Conformal Field Theory

  2001cites this paper
• An algebraic approach to logarithmic conformal field theory

  2001cites this paper
• Operator product expansion in logarithmic conformal field theory

  2001cites this paper