Logarithmic two-point correlators in the Abelian sandpile model

We present the detailed calculations of the asymptotics of two-site correlation functions for height variables in the two-dimensional Abelian sandpile model. By using combinatorial methods for the enumeration of spanning trees, we extend the well-known result for the correlation σ1,1≅1/r4 of minimal heights h1 = h2 = 1 to σ1,h = P1,h − P1Ph for height values h = 2, 3, 4. These results confirm the dominant logarithmic behaviour σ1,h≅(ch log r+dh)/r4+O(r-5) for large r, predicted by logarithmic conformal field theory based on field identifications obtained previously. We obtain, from our lattice calculations, the explicit values for the coefficients ch and dh (the latter are new)