Directed percolation in the two-dimensional continuum

We report the first study of directed percolation in the continuum. The percolation threshold is found to be at $B_c$=5.0±0.1, where $B_c$ is the average number of intersections per diode at the threshold. This is to be compared with $B_c$=3.2±0.1 in the corresponding nondirected problem. It is found that the critical exponents of this system are ${\nu }_{\mathrm{para}}$=0.74±0.05, ${\nu }_{\perp }$=0.46±0.08, β=0.33±0.07, and β’=(2.00 ±0.05)β. The good agreement with values found for directed lattices appears to be a confirmation of universality for these systems as well as a demonstration that geometrical and physical properties of directed systems in the continuum can be computed.