Anomalously rough sandpiles models in one dimension: exact decimation results

Abstract

We categorize the possible large-scale behaviors of one-dimensional nearest-neighbor hopping "sandpile" slope models on a circle of N sites with nonconserving noise, via decimation. Defining the height at site i to be h_i, we find a continuous infinity of fixed points of the decimation, parametrized by an index n (1≤n≤2) with <(h₀-h_N/2)²> ∼N^2/n. The fixed point n=2 corresponds to our ordinary notion of a rough interface, while the others are new and far rougher.