Generating functions for connected embeddings in a lattice. IV. Site percolation
- 21 August 1986
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 19 (12) , 2431-2437
- https://doi.org/10.1088/0305-4470/19/12/027
Abstract
For pt.III see ibid., vol.19, p.2425-9, 1986. The method of partial generating functions is applied to the problem of site percolation. It is concluded that the direct generation of site perimeter polynomials, although feasible, is likely to be less efficient than the corresponding generation of bond perimeter polynomials. The theory of percolation on a bipartite graph is developed and an alternative method of expanding the mean number of clusters for both site and bond mixtures without recourse to perimeter polynomials is described; a general prescription for the required generating functions is given.Keywords
This publication has 6 references indexed in Scilit:
- Generating functions for connected embeddings in a lattice. III. Bond percolationJournal of Physics A: General Physics, 1986
- Generating functions for connected embeddings in a lattice. II. Weak embeddingsJournal of Physics A: General Physics, 1986
- Generating functions for connected embeddings in a lattice. I. Strong embeddingsJournal of Physics A: General Physics, 1986
- Percolation processes in three dimensionsJournal of Physics A: General Physics, 1976
- Percolation processes in two dimensions. I. Low-density series expansionsJournal of Physics A: General Physics, 1976
- Percolation Processes. I. Low-Density Expansion for the Mean Number of Clusters in a Random MixtureJournal of Mathematical Physics, 1966