Series expansion for a stochastic sandpile

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.

Extended series and improved analysis

References in corpus (13)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• The universality class of absorbing phase transitions with a conserved field
• Self-organized criticality as an absorbing-state phase transition
• Low-density series expansions for directed percolation I: A new efficient algorithm with applications to the square lattice
• Absorbing-state phase transitions in fixed-energy sandpiles
• Driving, conservation and absorbing states in sandpiles
• Critical behavior of a one-dimensional fixed-energy stochastic sandpile
• Sandpiles with height restrictions
• Scaling behavior of the absorbing phase transition in a conserved lattice gas around the upper critical dimension
• Universality class of nonequilibrium phase transitions with infinitely many-absorbing-states
• Scaling behavior of the conserved transfer threshold process
• Path-integral representation for a stochastic sandpile
• Generic slow relaxation in a stochastic sandpile

Cited by in corpus (5)

• Solution of a model of self-avoiding walks with multiple monomers per site on the Bethe lattice
• Steady state of Stochastic Sandpile Models
• Approximation scheme for master equations: variational approach to multivariate case
• Asymptotic behavior of the order parameter in a stochastic sandpile
• A field theoretic approach to master equations and a variational method beyond the Poisson ansatz