Some results and a conjecture for Manna's stochastic sandpile model

Dhar, Deepak (1999) Some results and a conjecture for Manna's stochastic sandpile model Physica A: Statistical Mechanics and its Applications, 270 (1-2). pp. 69-81. ISSN 0378-4371

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We present some analytical results for the stochastic sandpile model studied earlier by Manna. In this model, the operators corresponding to particle addition at different sites commute. The eigenvalues of operators satisfy a system of coupled polynomial equations. For an L×L square, we construct a nontrivial toppling invariant, and hence a ladder operator which acting on eigenvectors of the evolution operator gives new eigenvectors with different eigenvalues. For periodic boundary conditions in one direction, one more toppling invariant can be constructed. We show that there are many forbidden subconfigurations, and only an exponentially small fraction of all stable configurations are recurrent. We obtain rigorous lower and upper bounds for the minimum number of particles in a recurrent configuration, and conjecture a formula for its exact value for finite-size rectangles.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Sandpile Model; Self-organized Criticality; Manna Model; Toppling Invariants; Forbidden Configuration; Minimal Configurations
ID Code:9286
Deposited On:29 Oct 2010 12:06
Last Modified:16 May 2016 19:06

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