Anisotropic Percolation on Slabs

Abstract

We consider anisotropic independent bond percolation models on the slab ${\mathbb{Z}}^2\times \{0,\dots ,k\}$, where we suppose that the axial (vertical) bonds are open with probability $p$, while the radial (horizontal) bonds are open with probability $q$. We study the critical curves for these models and establish their continuity and strict monotonicity.

7 pages

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