Logarithmic two-point correlators in the Abelian sandpile model
(2010) Journal Of Statistical Mechanics-theory And Experiment — (2010)
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- Abstract
- We present the detailed calculations of the asymptotics of two-site correlation functions for height variables in the two-dimensional Abelian sand pile model. By using combinatorial methods for the enumeration of spanning trees, we extend the well-known result for the correlation sigma(1,1) similar or equal to 1/r(4) of minimal heights h(1) = h(2) = 1 to sigma(1,h) = P-1,(h) - P1Ph for height values h = 2, 3, 4. These results confirm the dominant logarithmic behaviour sigma(1,h) similar or equal to (c(h) log r + d(h))/r(4) + 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 c(h) and d(h) (the latter are new).
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Poghosyan, V., Grigorev, S. Y., Priezzhev, V. B., & Ruelle, P. (2010). Logarithmic two-point correlators in the Abelian sandpile model. Journal Of Statistical Mechanics-theory And Experiment. Published. https://doi.org/10.1088/1742-5468/2010/07/P07025 (Original work published 2010)