Surface fluctuations and criticality in a class of one-dimensional sandpile models

We study the surface fluctuations of the one-dimensional limited local sandpile (LLS), a numerical model that exhibits self-organized criticality. We argue that certain apparently anomalous features can be understood when the model is viewed as a limiting case of a family of noncritical models. The criticality of the LLS is shown to result from a hidden symmetry which may not be present in real sandpiles.