I. Jensen et Aj. Guttmann, SERIES EXPANSIONS OF THE PERCOLATION PROBABILITY FOR DIRECTED SQUARE AND HONEYCOMB LATTICES, Journal of physics. A, mathematical and general, 28(17), 1995, pp. 4813-4833
We have derived long series expansions of the percolation probability
fbr site anti bond percolation on directed square and honeycomb lattic
es. For the square bond problem we have extended the series from 41 te
rms to 54, for the square site problem from 16 terms to 37, and for th
e honeycomb bond problem from 13 terms to 36. Analysis of the series c
learly shows that the critical exponent beta is the same fdr all the p
roblems, confirming expectations of universality. For the critical pro
bability and exponent we find in the square bond case, q(c) = -0.35529
94 +/- 0.0000010, beta = 0.27643 +/- 0.00010; in the square site case
q(c) = 0.294515 +/- 0.000005, beta = 0.2763 +/- 0.0003; and in the hon
eycomb bond case q(c) = 0.177143 +/- 0.000002, beta = 0.2763 +/- 0.000
2. In addition we have obtained accurate estimates for the critical am
plitudes. In all cases we find that the leading correction to scaling
term is analytic, i.e. the confluent exponent Delta = 1.