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

摘要: $n$-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 ${z}_{i}l~2).$ (This yields considerable simplification over unrestricted case, which states per unbounded.) On basis results $nl~11$ sites, critical particle density as ${\ensuremath{\zeta}}_{c}=0.930(1)$ estimated, good agreement with simulations. coherent anomaly analysis estimates order parameter exponent $[\ensuremath{\beta}=0.41(1)]$ and relaxation time $({\ensuremath{\nu}}_{||}\ensuremath{\simeq}2.5).$