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

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 $5^{th}$ 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.

20 pages, 8 figures

References in corpus (2)

• Low-density series expansions for directed percolation I: A new efficient algorithm with applications to the square lattice
• Series expansions of the percolation probability on the directed triangular lattice

Cited by in corpus (9)

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• Critical probabilities and convergence time of Percolation Probabilistic Cellular Automata
• Crossover scaling in the Domany-Kinzel cellular automaton
• Entropy Governed by the Absorbing State of Directed Percolation
• Hidden percolation transition in kinetic replication process
• Extended-range percolation in five dimensions