Anisotropic Percolation on Slabs

#### R.G. Couto, R. Sanchis, B.N.B. de Lima

2014, v.20, №1, 145-154

ABSTRACT

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

Keywords: long range percolation,percolation threshold