Logarithmic scaling for height variables in the Abelian sandpile model

Geoffroy Piroux; Philippe Ruelle

doi:10.1016/j.physletb.2004.12.045

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Logarithmic scaling for height variables in the Abelian sandpile model

Geoffroy Piroux·Philippe Ruelle

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Abstract

We report on the exact computation of the scaling form of the 1-point function, on the upper-half plane, of the height 2 variable in the two-dimensional Abelian sandpile model. By comparing the open versus the closed boundary condition, we find that the scaling field associated to the height 2 is a logarithmic scalar field of scaling dimension 2, belonging to a c=-2 logarithmic conformal field theory. This identification is confirmed by numerical simulations and extended to the height 3 and 4 variables, which exhibit the same scaling form. Using the conformal setting, we make precise proposals for the bulk 2-point functions of all height variables.

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Geoffroy Piroux, Philippe Ruelle. 2004-10-11. Logarithmic scaling for height variables in the Abelian sandpile model. https://doi.org/10.1016/j.physletb.2004.12.045

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