Universal correlations in the Abelian sandpile model
Abstract
We numerically study the bulk correlation functions in the two-dimensional Abelian sandpile model, aiming both to compare with the predictions of logarithmic conformal field theory and to extend the analysis to lattices where analytical methods are difficult to apply. Wilson's algorithm efficiently generates large-scale uniform spanning trees in parallel, which can be mapped to independent recurrent configurations via the Majumdar--Dhar burning bijection, eliminating sample autocorrelations and yielding fast convergence. On the square (single-sublattice) and honeycomb (two-sublattice) lattices our results agree well with the analytical predictions. For the kagome lattice we provide the first systematic numerical study of the bulk correlation functions, and cross-check the bulk height-1 probability against a closed-form analytical expression that we also derive here via the lattice Green function.
Related
- Avalanches of the Abelian sandpile on the hierarchical lattice
- The universal valued Abelian groups of Niemiec are Lévy, strongly exotic, extremely amenable, and 𝔾r(0) is generically monothetic
- On the structure of the sandpile identity element on Sierpiński gasket graphs.
- Avalanche homology of digraphs via sandpile dynamics
- Sandpile avalanches in two dimensions are finite
BibTeX
@misc{liu2026universal,
title = {{Universal correlations in the Abelian sandpile model}},
author = {Qiyu Liu and Jan-Niklas Herre and Prajit Baruah and Sebastian Dreizler and Christoph Karrasch and Wioletta Ruszel and Dirk Schuricht},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10352},
eprint = {2609.10352},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10352},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Universal correlations in the Abelian sandpile model
AU - Qiyu Liu
AU - Jan-Niklas Herre
AU - Prajit Baruah
AU - Sebastian Dreizler
AU - Christoph Karrasch
AU - Wioletta Ruszel
AU - Dirk Schuricht
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10352
UR - https://arxiv.org/abs/2609.10352
AB - We numerically study the bulk correlation functions in the two-dimensional Abelian sandpile model, aiming both to compare with the predictions of logarithmic conformal field theory and to extend the analysis to lattices where analytical methods are difficult to apply. Wilson's algorithm efficiently generates large-scale uniform spanning trees in parallel, which can be mapped to independent recurrent configurations via the Majumdar--Dhar burning bijection, eliminating sample autocorrelations and yielding fast convergence. On the square (single-sublattice) and honeycomb (two-sublattice) lattices our results agree well with the analytical predictions. For the kagome lattice we provide the first systematic numerical study of the bulk correlation functions, and cross-check the bulk height-1 probability against a closed-form analytical expression that we also derive here via the lattice Green function.
ER -