Abstract
We consider the directed Abelian sandpile model in the presence of sink sites whose density ft at depth t below the top surface varies as ct−χ. For χ>1 the disorder is irrelevant. For χ<1, it is relevant and the model is no longer critical for any nonzero c. For χ=1 the exponents of the avalanche distributions depend continuously on the amplitude c of the disorder. We calculate this dependence exactly, and verify the results with simulations.
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Lübeck, S., Dhar, D. Continuously Varying Exponents in a Sandpile Model with Dissipation Near Surface. Journal of Statistical Physics 102, 1–14 (2001). https://doi.org/10.1023/A:1026538607311
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DOI: https://doi.org/10.1023/A:1026538607311