Precise calculation of the threshold of various directed percolation models on a square lattice

Abstract

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.

2 pages, 2 figures and 1 table