Percolation exponent δpfor lattice dimensionality d⩾3
- 1 May 1977
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 10 (5) , 807-812
- https://doi.org/10.1088/0305-4470/10/5/014
Abstract
Series expansions are used to study the exponent delta p for site and bond percolation problems on three-dimensional lattices. The results, which include delta p=5.0+or-0.8, are discussed in relation to scaling theory and universality. To test Toulouse's conjecture (1974) regarding the critical dimensionality (dc=6) for percolation processes, a similar analysis is attempted for the site problem on simple hypercubical lattices of dimensionality 4<or=d<or=7.Keywords
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