Absence of site percolation at criticality in Z^2 x {0,1}
  In this note we consider site percolation on a two dimensional sandwich of thickness two, the graph Z^2 x {0,1}. We prove that there is no percolation at the critical point. The same arguments are valid for a sandwich of thickness three with periodic boundary conditions. It remains an open problem to extend this result to other sandwiches. 
Michael Damron, Charles M. Newman, Vladas Sidoravicius
math.PR