Asymptotic Behavior of the Order Parameter in a Stochastic Sandpile

We derive the first four terms in a series for the order paramater (the stationary activity density ) in the supercritical regime of a one-dimensional stochastic sandpile; in the two-dimensional case the first three terms are reported. This is done by reorganizing the pertubation theory derived using a path-integral formalism Dickman and Vidigal, J. Phys. A 35, 7269 (2002)], to obtain an expansion for stationary properties. Since the process has a strictly conserved particle density p, the Fourier mode N^-1 _k=0 p, when N , and so is not a random variable. Isolating this mode, we obtain a new effective action leading to an expansion for in the parameter 1/(1+4p). This requires enumeration and numerical evaluation of more than 200,000 diagrams, for which task we develop a computational algorithm. Predictions derived from this series are in good accord with simulation results. We also discuss the nature of correlation functions and one-site reduced distributions in the small- (high-density) limit.