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N-Site approximations and CAM analysis for a stochastic sandpile

Ronald Dickman
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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 z_i \leq 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 \leq 11 sites, I estimate the critical particle density as zeta_c = 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_|| \simeq 2.5).

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Ronald Dickman. 2002-04-29. N-Site approximations and CAM analysis for a stochastic sandpile. https://doi.org/10.1103/physreve.66.036122

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