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

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

2004-05-21

arxiv.org/abs/cond-mat/0405504v1

J. Phys. A 37, 6899-6915 (2004)

Physics

Condensed Matter

Statistical Mechanics

20 pages, 8 figures

Scientific paper

10.1088/0305-4470/37/27/003

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.

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