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Continuously Varying Exponents in a Sandpile Model with Dissipation Near Surface

Authors:	S. Lübeck D. Dhar

Affiliation:	(1) Theoretische Tieftemperaturphysik, Gerhard–Mercator-Universität Duisburg, Lotharstr. 1, 47048 Duisberg, Germany;(2) Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400005, India

Abstract:	We consider the directed Abelian sandpile model in the presence of sink sites whose density f_t at depth t below the top surface varies as ct^–. For >1 the disorder is irrelevant. For <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.

Keywords:	self-organized criticality directed Abelian sandpile model surface critical phenomena non-universal scaling behavior
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