N-Site approximations and CAM analysis for a stochastic sandpile

I develop n-site cluster approximations for a stochastic sandpile in one dimension. A height restriction is imposed to limit the number of states: each site can harbor at most two particles (height zi ≤ 2). (This yields a considerable simplification over the unrestricted case, in which the number of states per site is unbounded.) On the basis of results for n ≤ 11 sites, I estimate the critical particle density as ζc = 0.930(1), in good agreement with simulations. A coherent anomaly analysis yields estimates for the order parameter exponent [β = 0.41(1)] and the relaxation time exponent (ν|| ≃ 2.5). Typeset using REVTEX