n-site approximations and coherent-anomaly-method analysis for a stochastic sandpile.

n-site cluster approximations for a stochastic sandpile in one dimension are developed. A height restriction is imposed to limit the number of states: each site can harbor at most two particles (height z(i)< or =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< or =11 sites, the critical particle density as zeta(c)=0.930(1) is estimated, 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(//) approximately 2.5).

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