https://doi.org/10.1007/s100510051101
An analytical method to compute an approximate value of the site percolation threshold pc
CEA, DSM/DAPNIA/Service de Physique des Particules,
CE-Saclay, 91191 Gif-sur-Yvette Cedex, France
Received:
27
July
1999
Revised:
29
November
1999
Published online: 15 May 2000
An analytical method to compute the site percolation threshold is introduced. This method yields an approximate value of pc larger or equal to the real value. As examples, the computation of pc is presented for 4 lattices in 2 dimensions: square, triangular, honeycomb and kagome. The results obtained are 0.592 871 6, 0.5, 0.765 069, 0.654 653 7, to be compared with the real values 0.592 746 0, 0.5, 0.697 043, 0.652 703 6. The method is not limited to 2 dimensions.
PACS: 05.70.Fh – Phase transitions: general studies / 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions / 64.60.Fr – Equilibrium properties near critical points, critical exponents
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
