An upper bound on the critical percolation probability for the three- dimensional cubic lattice. (English) Zbl 0567.60096

The authors prove that the critical probability of percolation on the 3- dimensional cubic lattice is strictly less than \(1/2\). To prove this inequality a method of comparison of critical probabilities for different lattices is used, as well as some modification of Kesten’s method. The technique of the work admits a generalization to the 3-dimensional Ising model.
Reviewer: V.Chulaevsky


60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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