Absence of infinite cluster for critical Bernoulli percolation on slabs
  We prove that for Bernoulli percolation on a graph $\mathbb{Z}^2\times\{0,\dots,k\}$ ($k\ge 0$), there is no infinite cluster at criticality, almost surely. The proof extends to finite range Bernoulli percolation models on $\mathbb{Z}^2$ which are invariant under $\pi/2$-rotation and reflection. 
Hugo Duminil-Copin and Vladas Sidoravicius and Vincent Tassion
math.PR math-ph math.MP