Anisotropic Percolation on Slabs

TL;DR

This paper investigates anisotropic bond percolation on slab structures, analyzing how the critical probabilities depend on different bond types and establishing key properties of the critical curves.

Contribution

It introduces a detailed study of anisotropic percolation on slabs, proving continuity and strict monotonicity of the critical curves with respect to bond probabilities.

Findings

Critical curves are continuous functions of bond probabilities.

Critical curves are strictly monotonic.

The model extends understanding of anisotropic percolation behavior.

Abstract

We consider anisotropic independent bond percolation models on the slab $\Z^2\times\{0,\dots,k\}$, 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.