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Scaling fields in the two-dimensional Abelian sandpile model
1Université Catholique de Louvain, Institut de Physique Théorique, B-1348 Louvain-la-Neuve, Belgium.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
Summary
This study links the Abelian sandpile model to conformal field theory. Lattice correlations confirm predictions of a c=-2 conformal field theory, supporting local field theory descriptions.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Quantum Field Theory
Background:
- The Abelian sandpile model is a paradigm for self-organized criticality.
- Understanding critical phenomena often involves mapping to field theories.
Purpose of the Study:
- To investigate the Abelian sandpile model using two-dimensional conformal field theory.
- To compute lattice correlation functions and determine the scaling limit description.
Main Methods:
- Calculation of lattice correlation functions for cluster variables.
- Analysis of results in the scaling limit.
- Comparison with conformal field theory predictions.
Main Results:
- Perfect agreement was found between computed correlations and predictions of a c=-2 conformal field theory.
- Direct evidence for conformal invariance in the model was obtained.
- Support for a local field theory description was established.
Conclusions:
- The unoriented two-dimensional Abelian sandpile model exhibits conformal invariance at criticality.
- The model can be described by a c=-2 conformal field theory and its massive perturbation.
- Further investigation is needed for the height 2 variable.