Numéro
J. Phys. I France
Volume 1, Numéro 5, May 1991
Page(s) 685 - 692
DOI https://doi.org/10.1051/jp1:1991162
DOI: 10.1051/jp1:1991162
J. Phys. I France 1 (1991) 685-692

Transport through bootstrap percolation clusters

Muhammad Sahimi and Tane S. Ray

Supercomputer Center HLRZ, c/o KFA Jülich, P.O. Box 1913, D-5170 Jülich 1, Germany


(Received 2 January 1991, accepted 17 January 1991)

Abstract
In bootstrap percolation (BP) on lattices sites are initially occupied at random. Those occupied sites that do not have at least m occupied nearest-neighbors are then removed. For sufficiently large values of m (e.g., $m\geqslant 4$ for the cubic lattice) first-order phase transitions occur at the percolation threshold, $p_{\rm c}$, while for small values of m the phase transition is second-order. We study conductivity of BP clusters as a function of m, the dimensionality of the system and its linear size L. This is relevant to spin-wave stiffness of disordered magnetic systems, e.g., the dilute Blume-Capel model and, as we argue here, it may also be relevant to the behavior of disordered solids that undergo a brittle fracture process, and to flow through a porous medium. On a cubic lattice we find that the conductivity critical exponent t for m=3 is the same as that of random percolation (m=0). Since for m=0-3 the correlation length exponent also remains unchanged, but the critical exponent $\beta$ of the strength of the infinite clusters is different for m=2 and 3, we argue that this indicates that for three-dimensional systems t cannot be related to $\beta$. For $m\geqslant 4$, the conductivity is discontinuous at $p_{\rm c}$, followed by a power-law jump, as the fraction of conducting material is increased, with a critical exponent that is apparently different from t.



© Les Editions de Physique 1991

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.