Universal correlations in the Abelian sandpile model

arXiv (Cornell University)

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.

Authors 7

1. Qiyu Liu

   Technische Universität Braunschweig

   Affiliation as printed

   Technische Universität Braunschweig , Institut für Mathematische Physik , Mendelssohnstrasse 3 , 38106 Braunschweig , Germany

2. Jan-Niklas Herre Aachen Institute for Theory of Statistical Physics

   RWTH Aachen University

   Affiliation as printed

   Institute for Theory of Statistical Physics , RWTH Aachen University , Aachen , Germany

3. Prajit Baruah

   Utrecht University

   Affiliation as printed

   Institute for Theoretical Physics , Utrecht University , Princetonplein 5 , 3584 CE Utrecht , The Netherlands

4. Sebastian Dreizler

   Technische Universität Braunschweig

   Affiliation as printed

   Technische Universität Braunschweig , Institut für Mathematische Physik , Mendelssohnstrasse 3 , 38106 Braunschweig , Germany

5. Christoph Karrasch

   Technische Universität Braunschweig

   Affiliation as printed

   Technische Universität Braunschweig , Institut für Mathematische Physik , Mendelssohnstrasse 3 , 38106 Braunschweig , Germany

6. Wioletta M. Ruszel

   Utrecht University

   Affiliation as printed

   Mathematical Institute , Utrecht University , Budapestlaan 6 , 3584 CD Utrecht , The Netherlands

7. Dirk Schuricht

   Utrecht University

   Affiliation as printed

   Institute for Theoretical Physics , Utrecht University , Princetonplein 5 , 3584 CE Utrecht , The Netherlands