Series expansions for the directed-bond percolation problem

Abstract

Series expansion methods have been used to estimate the critical probability, p_c, and to investigate percolation behaviour for the directed-bond problem on most of the usual lattices. High-density series expansions of P(p) and low-density series expansions of S(p) were obtained for the acyclic directed square (SQ), triangular (T), SC, BCC and FCC lattices, and also the cyclic directed triangular lattice. The results suggest that directed models need not fall into the same universality class as the corresponding undirected models. The results for the acyclic and cyclic directed triangular lattices further suggest that different directings of the same lattice may yield models falling into different universality classes.