Abstract
We consider a dilute lattice obtained from the usual Z3 lattice by removing independently each of its columns with probability 1−ρ. In the remaining dilute lattice independent Bernoulli bond percolation with parameter p is performed. Let ρ↦pc(ρ) be the critical curve which divides the subcritical and supercritical phases. We study the behavior of this curve near the disconnection threshold ρc=pcsite(Z2) and prove that, uniformly over ρ it remains strictly below 1/2 (the critical point for bond percolation on the square lattice Z2).
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