Precise calculation of the threshold of various directed percolation   models on a square lattice
  Using Monte Carlo simulations on different system sizes we determine with high precision the critical thresholds of two families of directed percolation models on a square lattice. The thresholds decrease exponentially with the degree of connectivity. We conjecture that $p_{c}$ decays exactly as the inverse of the coodination number. 
Danyel J. B. Soares, Jose S. Andrade Jr., Hans J. Herrmann