Abelian Sandpile Model: a Conformal Field Theory Point of View

@article{MoghimiAraghi2005AbelianSM,
  title={Abelian Sandpile Model: a Conformal Field Theory Point of View},
  author={Saman Moghimi-Araghi and Morteza Rajabpour and Shahin Rouhani},
  journal={Nuclear Physics},
  year={2005},
  volume={718},
  pages={362-370}
}

Figures from this paper

Higher order and boundary scaling fields in the Abelian sandpile model
The Abelian sandpile model (ASM) is a paradigm of self-organized criticality (SOC) which is related to c = −2 conformal field theory. The conformal fields corresponding to some height clusters have
Holographic applications of logarithmic conformal field theories
We review the relations between Jordan cells in various branches of physics, ranging from quantum mechanics to massive gravity theories. Our main focus is on holographic correspondences between
Logarithmic conformal invariance in the Abelian sandpile model
We review the status of the two-dimensional Abelian sandpile model as a strong candidate to provide a lattice realization of logarithmic conformal invariance with a central charge c = −2. Evidence
The spatial asymmetric two-dimensional continuous Abelian sandpile model
We insert some asymmetries into the continuous Abelian sandpile models, such as directedness and ellipticity. We analyze probability distribution of different heights and also find the corresponding
The Logarithmic triplet theory with boundary
The boundary theory for the c = −2 triplet model is investigated in detail. In particular, we show that there are four different boundary conditions that preserve the triplet algebra and check the
Patterned and disordered continuous Abelian sandpile model.
TLDR
This work considers the continuous directed sandpile model perturbed by a weak quenched randomness, study critical behavior of the model using perturbative conformal field theory, and shows that the model has a random fixed point.
The Abelian sandpile model on the honeycomb lattice
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
Wind on the boundary for the Abelian sandpile model
We continue our investigation of the two-dimensional Abelian sandpile model in terms of a logarithmic conformal field theory with central charge c = −2, by introducing two new boundary conditions.
...
1
2
3
...

References

SHOWING 1-10 OF 62 REFERENCES
Scaling fields in the two-dimensional Abelian sandpile model.
  • S. Mahieu, P. Ruelle
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2001
TLDR
It is found that perfect agreement with the predictions of a c=-2 conformal field theory and its massive perturbation is found, thereby providing direct evidence for conformal invariance and more generally for a description in terms of a local field theory.
Boundary height fields in the Abelian sandpile model
We study the abelian sandpile model on the upper half plane, and reconsider the correlations of the four height variables lying on the boundary. For more convenience, we carry out the analysis in the
Conformal field theory correlations in the Abelian sandpile model.
  • M. Jeng
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2005
TLDR
The correlation functions show that all local bond modifications have scaling dimension 2, and can be written as linear combinations of operators in the central charge -2 logarithmic conformal field theory, in agreement with a form conjectured earlier by Mahieu and Ruelle.
Correlation functions of dense polymers and c=-2 conformal field theory
`Antisymmetric' correlation functions of the model of dense lattice polymers are proved to be given by the generalized Kirchhoff theorem. In the continuum limit they coincide with the correlation
Pre-logarithmic and logarithmic fields in a sandpile model
We consider the unoriented two-dimensional Abelian sandpile model on the half-plane with open and closed boundary conditions, and relate it to the boundary logarithmic conformal field theory with
Boundary height correlations in a two-dimensional Abelian sandpile
Boundary height distributions of the two-dimensional Abelian sandpile model are studied in the self-organized critical state. All height probabilities are calculated explicitly both at open and
...
1
2
3
4
5
...