Journal
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
Volume 156, Issue 2, Pages 263-279Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S030500411300073X
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Funding
- Swiss National Science Foundation
- EPSRC [EP/103372X/1]
- Israel Science Foundation
- EPSRC [EP/I03372X/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/I03372X/1] Funding Source: researchfish
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Two related issues are explored for bond percolation on Z(d) (with d >= 3) and its dual plaquette process. Firstly, for what values of the parameter p does the complement of the infinite open cluster possess an infinite component? The corresponding critical point p(fin) satisfies p(fin) >= p(c), and strict inequality is proved when either d is sufficiently large, or d >= 7 and the model is sufficiently spread out. It is not known whether d >= 3 suffices. Secondly, for what p does there exist an infinite dual surface of plaquettes? The associated critical point p(surf) satisfies p(surf) >= p(fin).
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