CORRELATIONS, MEAN-FIELD PROPERTIES, AND SCALING OF A ONE-DIMENSIONALSANDPILE MODEL

We present a general relationship between different scaling exponents for the one-dimensional sand-pile problem to describe the self-adjusti ng of the slope of the sandpile. We solve the mean-field theory for th is model, assuming that there is no correlation between the sizes of n eighbor clusters. The mean-field theory does not give the correct expo nents, since the clusters are strongly correlated. We characterize the se correlations, identify the functional form of the cluster distribut ion function, and show how the multifractal scaling for averaged quant ities arises from this form.