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arXiv · 1211.4138

Absence of site percolation at criticality in Z^2 x {0,1}

Michael Damron·Charles M. Newman·Vladas Sidoravicius
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Abstract

In this note we consider site percolation on a two dimensional sandwich of thickness two, the graph Z^2 x {0,1}. We prove that there is no percolation at the critical point. The same arguments are valid for a sandwich of thickness three with periodic boundary conditions. It remains an open problem to extend this result to other sandwiches.

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Michael Damron, Charles M. Newman, Vladas Sidoravicius. 2012-11-17. Absence of site percolation at criticality in Z^2 x {0,1}. https://arxiv.org/abs/1211.4138

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