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Updated: Jun 29, 2026

Determination of Aggregate Surface Morphology at the Interfacial Transition Zone (ITZ)
Published on: December 16, 2019
Percolation clusters above criticality form Kardar-Parisi-Zhang surfaces
1Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.
Abstract:
This study is concerned with the characteristics of regular (isotropic) percolation clusters above the critical threshold p{c}. 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.
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