Continuously varying exponents in a sandpile model with dissipation near surface

摘要

We consider the directed Abelian sandpile model in the presence of sink sites whose density f(l) at depth t below the top surface varies as ct(-chi). For chi >1 the disorder is irrelevant. For chi <1, it is relevant and the model is no longer critical for any nonzero c. For =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. [References: 21]