Multipoint correlators in the Abelian sandpile model

摘要: We revisit the calculation of height correlations in two-dimensional Abelian sandpile model by taking advantage a technique developed recently Kenyon and Wilson. The formalism requires to equip usual graph Laplacian, ubiquitous context cycle-rooted spanning forests, with complex connection. In case at hand, connection is constant localized along semi-infinite defect line (zipper). appropriate limit trivial connection, it allows one count forests whose components contain prescribed sites, which are direct relevance for model. Using this technique, we first rederive known 1- 2-site lattice correlators on plane upper half-plane, more efficiently than what has been done so far. also compute explicitly (new) next-to-leading order distances ($r^{-4}$ 1-site $r^{-6}$ plane). extend these results computing new involving arbitrary few heights 1 open closed boundary conditions. examine our from conformal point view, confirm full consistency specific features currently conjectured be present associated logarithmic field theory.