Series expansions of the percolation probability for directed square and honeycomb lattices

Abstract

We have derived long series expansions of the percolation probability for site and bond percolation on directed square and honeycomb lattices. For the square bond problem we have extended the series from 41 terms to 54, for the square site problem from 16 terms to 37, and for the honeycomb bond problem from 13 terms to 36. Analysis of the series clearly shows that the critical exponent $\beta$ is the same for all the problems confirming expectations of universality. For the critical probability and exponent we find in the square bond case, $q_c=0.3552994\pm 0.0000010$, $\beta =0.27643\pm 0.00010$, in the square site case $q_c=0.294515\pm 0.000005$, $\beta =0.2763\pm 0.0003$, and in the honeycomb bond case $q_c=0.177143\pm 0.000002$, $\beta =0.2763\pm 0.0002$. In addition we have obtained accurate estimates for the critical amplitudes. In all cases we find that the leading correction to scaling term is analytic, i.e., the confluent exponent $\Delta =1$.

LaTex with epsf, 26 pages, 2 figures and 2 tables in Postscript format included (uufiled). LaTeX version of tables also included for the benefit of those without access to PS printers (note that the tables should be printed in landscape mode). Accepted by J. Phys. A

References in corpus (1)

• Critical behaviour of a surface reaction model with infinitely many absorbing states

Cited by in corpus (12)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Low-density series expansions for directed percolation I: A new efficient algorithm with applications to the square lattice
• Smooth Phases, Roughening Transitions and Novel Exponents in One-dimensional Growth Models
• Multicritical behavior in coupled directed percolation processes
• High-precision Monte Carlo study of directed percolation in (d+1) dimensions
• Directed percolation near a wall
• Subcritical behavior in the alternating supercritical Domany-Kinzel dynamics
• Series expansions of the percolation probability on the directed triangular lattice
• Correlated Initial Conditions in Directed Percolation
• Low-density series expansions for directed percolation II: The square lattice with a wall
• On directed interacting animals and directed percolation