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arXiv · hep-th/0407143

Pre-logarithmic and logarithmic fields in a sandpile model

Geoffroy Piroux·Philippe Ruelle
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Abstract

We consider the unoriented two-dimensional Abelian sandpile model on the half-plane with open and closed boundary conditions, and relate it to the boundary logarithmic conformal field theory with central charge c=-2. Building on previous results, we first perform a complementary lattice analysis of the operator effecting the change of boundary condition between open and closed, which confirms that this operator is a weight -1/8 boundary primary field, whose fusion agrees with lattice calculations. We then consider the operators corresponding to the unit height variable and to a mass insertion at an isolated site of the upper half plane and compute their one-point functions in presence of a boundary containing the two kinds of boundary conditions. We show that the scaling limit of the mass insertion operator is a weight zero logarithmic field.

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Geoffroy Piroux, Philippe Ruelle. 2004-11-18. Pre-logarithmic and logarithmic fields in a sandpile model. https://doi.org/10.1088/1742-5468%2F2004%2F10%2Fp10005

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