Anomalously rough sandpiles in one dimension: Exact decimation results

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 ${\mathit{h}}_{\mathit{i}}$, we find a continuous infinity of fixed points of the decimation, parametrized by an index n (1≤n≤2) with 〈(${\mathit{h}}_0$-${\mathit{h}}_{\mathit{N}/2\mathrm{}}$${)}^2$〉∼${\mathit{N}}^{2/\mathit{n}}$. The fixed point n=2 corresponds to our ordinary notion of a rough interface, while the others are new and far rougher.