Has it been proved that the two dimensional semi-oriented percolation process exhibits a phase transition at $p_c < 1/2$ (STRICTLY less than 1/2!!)?
Semi-oriented Percolation: 2 dimensional lattice, where each edge directed on the right, on the left or up can be open with probability $p$ and closed with probability $(1 - p)$. The edge directed down is always closed. $\Theta(p)$ is the probability that the origin of the lattice is contained in an infinite cluster of vertices connected by open edges. $p_c$ is the sup of the values of p such that $\Theta(p)=0$.
1) $p_c \geq 1/2$ comes authomatically from the comparison with the standard percolation process.
2) for the oriented percolation (only the edges in directions up and right can be open, the 2 others are surely closed) it is proved that $p_c > 1/2$.