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Series expansion for a stochastic sandpile

Jurgen F. Stilck·Ronald Dickman·Ronaldo R. Vidigal
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Abstract

Using operator algebra, we extend the series for the activity density in a one-dimensional stochastic sandpile with fixed particle density p, the first terms of which were obtained via perturbation theory [R. Dickman and R. Vidigal, J. Phys. A35, 7269 (2002)]. The expansion is in powers of the time; the coefficients are polynomials in p. We devise an algorithm for evaluating expectations of operator products and extend the series to O(t^{16}). Constructing Pade approximants to a suitably transformed series, we obtain predictions for the activity that compare well against simulations, in the supercritical regime.

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Jurgen F. Stilck, Ronald Dickman, Ronaldo R. Vidigal. 2003-10-21. Series expansion for a stochastic sandpile. https://doi.org/10.1088/0305-4470%2F37%2F4%2F004

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