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 -