TY - JOUR
T1 - Structure of self-avoiding walks on percolation clusters at criticality
AU - Eduardo Roman, H.
AU - Ordemann, Anke
AU - Porto, Markus
AU - Bunde, Armin
AU - Havlin, Shlomo
PY - 1998/5
Y1 - 1998/5
N2 - The structure of linear polymers modelled by self-avoiding random walks (SAWs) on the backbone of two-dimensional percolation clusters at criticality is studied. To this end, all possible SAW configurations of N steps on a single-backbone configuration are enumerated exactly, and averages over many backbone configurations are performed to extract the mean quantities of interest. We determine the critical exponents describing the structure of SAWs, in both Euclidean and topological space, and the corresponding mean distribution functions for the end-to-end distance after N steps. A relation between the exponents characterizing the asymptotic shape of these distributions and those describing the total number of SAWS of N steps on the backbone is suggested and supported by numerical results.
AB - The structure of linear polymers modelled by self-avoiding random walks (SAWs) on the backbone of two-dimensional percolation clusters at criticality is studied. To this end, all possible SAW configurations of N steps on a single-backbone configuration are enumerated exactly, and averages over many backbone configurations are performed to extract the mean quantities of interest. We determine the critical exponents describing the structure of SAWs, in both Euclidean and topological space, and the corresponding mean distribution functions for the end-to-end distance after N steps. A relation between the exponents characterizing the asymptotic shape of these distributions and those describing the total number of SAWS of N steps on the backbone is suggested and supported by numerical results.
UR - http://www.scopus.com/inward/record.url?scp=0032072872&partnerID=8YFLogxK
U2 - 10.1080/13642819808205029
DO - 10.1080/13642819808205029
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AN - SCOPUS:0032072872
SN - 1364-2812
VL - 77
SP - 1357
EP - 1371
JO - Philosophical Magazine B: Physics of Condensed Matter; Statistical Mechanics, Electronic, Optical and Magnetic Properties
JF - Philosophical Magazine B: Physics of Condensed Matter; Statistical Mechanics, Electronic, Optical and Magnetic Properties
IS - 5
ER -