Low-density series expansions for directed percolation III. Some two-dimensional lattices

We use very efficient algorithms to calculate low-density series for bond and site percolation on the directed triangular, honeycomb, kagom\'e, and $(4.8^2)$ lattices. Analysis of the series yields accurate estimates of the critical point $p_c$ and various critical exponents. The exponent estimates differ only in the $5^{th}$ digit, thus providing strong numerical evidence for the expected universality of the critical exponents for directed percolation problems. In addition we also study the non-physical singularities of the series.Comment: 20 pages, 8 figure

Low-density series expansions for directed percolation I: A new efficient algorithm with applications to the square lattice

A new algorithm for the derivation of low-density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems. Numerical evidence shows that the computational complexity grows exponentially, but with a growth factor \lambda < \protect{\sqrt[8]{2}}, which is much smaller than the growth factor \lambda = \protect{\sqrt[4]{2}} of the previous best algorithm. For bond (site) percolation on the directed square lattice the series has been extended to order 171 (158). Analysis of the series yields sharper estimates of the critical points and exponents.Comment: 20 pages, 8 figures (3 of them > 1Mb

Low-density series expansions for directed percolation I: A new efficient algorithm with applications to the square lattice

A new algorithm for the derivation of low-density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems. Numerical evidence shows that the computational complexity grows exponentially, but with a growth factor \lambda < \protect{\sqrt[8]{2}}, which is much smaller than the growth factor \lambda = \protect{\sqrt[4]{2}} of the previous best algorithm. For bond (site) percolation on the directed square lattice the series has been extended to order 171 (158). Analysis of the series yields sharper estimates of the critical points and exponents.Comment: 20 pages, 8 figures (3 of them > 1Mb