We study the asymptotic shape of self-avoiding random walks (SAW) on the backbone of the incipient percolation cluster in d-dimensional lattices analytically. It is generally accepted that the configurational averaged probability distribution function 〈PB(r,N)〈 for the end-to-end distance r of an N step SAW behaves as a power law for r→0. In this work, we determine the corresponding exponent using scaling arguments, and show that our suggested "generalized des Cloizeaux" expression for the exponent is in excellent agreement with exact enumeration results in two and three dimensions. ©2001 The American Physical Society.
Ordemann, A., Porto, M., Eduardo Roman, H., Havlin, S. (2001). "Generalized des Cloizeaux" exponent for self-avoiding walks on the incipient percolation cluster. PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS, 63(2 I), 0201041-0201043 [10.1103/PhysRevE.63.020104].
"Generalized des Cloizeaux" exponent for self-avoiding walks on the incipient percolation cluster
Eduardo Roman H.;
2001
Abstract
We study the asymptotic shape of self-avoiding random walks (SAW) on the backbone of the incipient percolation cluster in d-dimensional lattices analytically. It is generally accepted that the configurational averaged probability distribution function 〈PB(r,N)〈 for the end-to-end distance r of an N step SAW behaves as a power law for r→0. In this work, we determine the corresponding exponent using scaling arguments, and show that our suggested "generalized des Cloizeaux" expression for the exponent is in excellent agreement with exact enumeration results in two and three dimensions. ©2001 The American Physical Society.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.