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

1999/01/01 by Iwan Jensen · 9 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Cellular Automata and Applications #Critical exponent #Directed percolation #Geometry #Lattice (music) #Mathematical analysis #Mathematics #Percolation (cognitive psychology) #Percolation threshold #Physics #Quantum mechanics #Scaling #Series (stratigraphy) #Series expansion #Square (algebra) #Square lattice #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1088/0305-4470/32/28/304

20 pages, 8 figures (3 of them > 1Mb)

openalex publication_date 1999/01/01 · arxiv created 1999/06/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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 < , which is much smaller than the growth factor = 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.

Citations

• Nonequilibrium critical behavior in unidirectionally coupled stochastic processes
• Chiral Potts Models, Friendly Walkers and Directed Percolation Problem

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