Logarithmic two-point correlators in the Abelian sandpile model

Abstract

We present the detailed calculations of the asymptotics of two-site correlation functions forheight variables in the two-dimensional Abelian sandpile model. By using combinatorialmethods for the enumeration of spanning trees, we extend the well-known result for thecorrelation of minimal heights h1 = h2 = 1 to σ1, h = P1, h − P1Ph forheight values h = 2, 3, 4. These results confirm the dominant logarithmic behaviour for large r, predicted by logarithmic conformal field theory based on field identifications obtainedpreviously. We obtain, from our lattice calculations, the explicit values for the coefficientsch anddh (the latter are new).