Directed percolation, fractal roots and the Lee–Yang theorem

In the directed percolation model we consider the probability p of having an open bond as a complex parameter. We show that the roots of the survival probability PN(p) for a square lattice of N rows distribute themselves in a fractal manner in the complex p-plane. These roots have an accumulation point on the real axis which coincides with the critical probability pc=0.6447.