I Jensen and A J Guttmann 1995 J. Phys. A: Math. Gen. 28 4813 doi:10.1088/0305-4470/28/17/015
I Jensen and A J Guttmann
Show affiliationsWe 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, qc=0.3552994+or-0.0000010, beta =0.27643+or-0.00010; in the square site case qc= 0.294515+or-0.000005, beta =0.2763+or-0.0003; and in the honeycomb bond case qc=0.177143+or-0.000002, beta =0.2763+or-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.
64.60.A- Specific approaches applied to studies of phase transitions
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
02.30.Mv Approximations and expansions
02.30.Lt Sequences, series, and summability
64.60.F- Equilibrium properties near critical points, critical exponents
82B43 Percolation (See also 60K35)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
Issue 17 (7 September 1995)
I Jensen and A J Guttmann 1995 J. Phys. A: Math. Gen. 28 4813
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