Properties of infinite clusters in general percolation models are investigated. The number of infinite clusters is either zero, one or infinity. Results are found on the density of the various kinds of infinite clusters. In particular, 'filamentary' and 'rough' clusters, which individually do not have non-zero density, are studied with an eye toward ascertaining whether these exist in some models, and hence whether an infinity of infinite clusters is possible. Conjectures are presented on the behaviour of systems with an infinity of infinite clusters under scale transformations, and also on the way in which the presence of such clusters influences the prevalence of large finite clusters.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)