N-Site approximations and CAM analysis for a stochastic sandpile
Ronald Dickman
Abstract
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 zetac = 0.930(1), in good agreement with simulations. A coherent anomaly analysis yields estimates for the order parameter exponent [beta = 0.41(1)] and the relaxation time exponent (nu|| 2.5).
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