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

Iwan Jensen

doi:10.1088/0305-4470/37/27/003

paper

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

arXiv:cond-mat/0405504 · doi:10.1088/0305-4470/37/27/003

Abstract

We use very efficient algorithms to calculate low-density series for bond and site percolation on the directed triangular, honeycomb, kagomé, 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 $5^{t h}$ 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.

20 pages, 8 figures