Exact solution of a one-dimensional deterministic sandpile model.

Using the transfer matrix method, we give the exact solution of a deterministic sandpile model for arbitrary N , where N is the size of a single toppling. The oneand two-point functions are given in term of the eigenvalues of an N × N transfer matrix. All the n-point functions can be found in the same way. Application of this method to a more general class of models is discussed. We also present a quantitative description of the limit cycle (attractor) as a multifractal. PACS number(s):05.40.+j, 05.70.Jk, 05.70.Ln Typeset using REVTEX 1