TY - JOUR
T1 - Percolation clusters above criticality form Kardar-Parisi-Zhang surfaces
AU - Perlsman, Ehud
AU - Havlin, Shlomo
PY - 2008/9/30
Y1 - 2008/9/30
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=53449083090&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.101.145701
DO - 10.1103/PhysRevLett.101.145701
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AN - SCOPUS:53449083090
SN - 0031-9007
VL - 101
JO - Physical Review Letters
JF - Physical Review Letters
IS - 14
M1 - 145701
ER -