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

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.

• Publication year

  1999

• Venue

  Physica A-statistical Mechanics and Its Applications

• Publication date

  1999-02-10

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1016/S0378-4371(99)00149-1arXiv cond-mat/9902137
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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