Logarithmic scaling for height variables in the Abelian sandpile model
(2004) Physics Letters. Section B: Nuclear, Elementary Particle and High-Energy Physics — Vol. B607, p. 188-196 (2005)
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- (en) 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. Comment: 7 pages, 2 figures
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Piroux, G., & Ruelle, P. (2004). Logarithmic scaling for height variables in the Abelian sandpile model. Physics Letters. Section B: Nuclear, Elementary Particle and High-Energy Physics, B607, 188-196. https://doi.org/10.1016/j.physletb.2004.12.045 (Original work published 2005)