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.
Mahieu
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Université Catholique de Louvain, Institut de Physique Théorique, B-1348 Louvain-la-Neuve, Belgium.
Ruelle
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