Scaling fields in the two-dimensional Abelian sandpile model.
(2001) Physical review. E, Statistical, nonlinear, and soft matter physics — Vol. 64, n° 6 Pt 2, p. 66130 (2001)
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- 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.
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Mahieu, S., & Ruelle, P. (2001). Scaling fields in the two-dimensional Abelian sandpile model. Physical review. E, Statistical, nonlinear, and soft matter physics, 64(6 Pt 2), 66130. https://doi.org/10.1103/PhysRevE.64.066130 (Original work published 2001)