Issue |
J. Phys. I France
Volume 3, Number 10, October 1993
|
|
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Page(s) | 2007 - 2016 | |
DOI | https://doi.org/10.1051/jp1:1993228 |
J. Phys. I France 3 (1993) 2007-2016
Series studies of self-avoiding walks near the
-points on 2D and 3D clusters at the percolation thresholds
K. Barat, S. N. Karmakar and B. K. Chakrabarti Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta 700064, India
(Received 12 May 1993, accepted in final form 22 June 1993)
Abstract
Enumerating all the
N-stepped SAW configurations on the infinite percolation cluster of Monte Carlo generated bond diluted lattices (in dimension
d = 2 as well as in
d = 3) at the respective percolation thresholds, the thermally weighted average end-to-end distance
of self-interacting self-avoiding walks are determined. The configurationally averaged
(over different percolation clusters) are then fitted to a scaling form
, where
denotes the temperature interval away from the
-point,
is the tricritical (
-point) size exponent,
is the crossover exponent and
f is the scaling function. From the best fit, the values of
,
and
are obtained for the 2D and 3D lattices considered. We find
and
for the tricritical exponents on the percolation clusters (at the percolation thresholds) in dimensions
d = 2 and
d = 3 respectively. We also find theta-temperature
,
and
for bond dilute square, triangular and simple cubic lattices respectively on the critical percolation clusters. Our scaling
fit results for
-point and the
values for various percolating lattices are then compared with some theoretical (mean field-like) estimates.
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