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Absence of infinite cluster for critical Bernoulli percolation on slabs. (English) Zbl 1342.82076
Summary: We prove that for Bernoulli percolation on a graph $$\mathbb{Z}^2\times\{0,\dots,k\}$$ $$(k\geq0)$$, there is no infinite cluster at criticality, almost surely. The proof extends to finite-range Bernoulli percolation models on $$\mathbb{Z}^2$$ that are invariant under $${\frac{\pi}2}$$-rotation and reflection.

##### MSC:
 82B43 Percolation 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B26 Phase transitions (general) in equilibrium statistical mechanics
##### Keywords:
Bernoulli percolation
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##### References:
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