Percolation clusters above criticality form Kardar-Parisi-Zhang surfaces

This study is concerned with the characteristics of regular (isotropic) percolation clusters above the critical threshold pc. Analytic arguments for the general dimension case, and numerical results for the two-dimensional case, lead to the conclusion that the characteristics of the shortest paths (defined as the chemical distance l) between given two sites on a percolation cluster are similar to the characteristics of optimal paths in the directed polymer model. A corollary which should be valid for the general dimension case, and verified by numerical results for the two-dimensional case, is that a cluster whose sites are at chemical distance l from a given site forms a Kardar-Parisi-Zhang surface.