An analytical method to compute an approximate value of the site percolation threshold pc

European Physical Journal B

Volumn 15, Issue 1, 2000, Pages 77-86

  Rosowsky, A ^a  

^a CEA SACLAY   (France)

Author keywords

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

Indexed keywords

EID: 0011242725     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1007/pl00011036     Document Type: Article

References (50)

1. D. Stauffer, A. Aharony, Introduction to Percolation Theory, Revised 2nd edn. (Taylor and Francis, London, 1994).
2. A.L. Barbarsi, H.E. Stanley, Fractal Concepts In Surface Growth (Cambridge Univ. Press, Cambridge, 1995).
3. S.W. Golomb, Polyominoes: Puzzles, Patterns, Problems, and Packings, Revised edn. (Princeton Univ. Press, Princeton, 1994).
4. S.R. Broadbent, J. R. Stat. Soc. B 16, 68 (1954).
5. S.R. Broadbent, J.M. Hammersley, Proc. Camb. Philos. Soc. 53, 629 (1957).
6. J.W. Essam, M.F. Sykes, J. Math. Phys. (N.Y.) 5, 1117 (1964).
7. C.M. Fortuin, P.W. Kasteleyn, Physica 57, 536 (1971).
8. J. Hoshen, R. Kopelman, Phys. Rev. B 14, 3438 (1976).
9. J.C. Wierman, J. Phys. A 17, 1525 (1984).
10. R.M. Ziff, Phys. Rev. Lett. 56, 545 (1986).
11. J.C. Wierman, J. Phys. A 21, 1487 (1988).
12. C. Dussert, G. Rasigni, M. Rasigni, Phys. Lett. A 139, 35 (1989).
13. F. Yonezawa, S. Sakamoto, Motoo Hori, Phys. Rev. B 40, 636 (1989).
14. F. Yonezawa, S. Sakamoto, Motoo Hori, Phys. Rev. B 40, 650 (1989).
15. J.L. Cardy, J. Phys. A 25, L201 (1992).
16. R.M. Ziff, Phys. Rev. Lett. 69, 2670 (1992).
17. R.P. Langlands, C. Pichet, Ph. Pouliot, Y. Saint-Aubin, J. Stat. Phys. 67, 553 (1992).
18. S. Galam, A. Mauger, J. Appl. Phys. 75, 5526 (1994).
19. S. Galam, A. Mauger, Physica A 205, 502 (1994).
20. C. d'Iribarne, G. Rasigni, M. Rasigni, Phys. Lett. A 209, 95 (1995).
21. I. Jensen, A.J. Gutmann, J. Phys. A 28, 4813 (1995).
22. S. Galam, A. Mauger, Phys. Rev. E 53, 2177 (1996).
23. S. Galam, A. Mauger, Phys. Rev. E 55, 1230 (1997).
24. S.C. van der Marck, Phys. Rev. E 55, 1228 (1997).
25. S.C. van der Marck, Phys. Rev. E 55, 1514 (1997).
26. S. Galam, A. Mauger, Phys. Rev. E 56, 322 (1997).
27. M. Aizenman, Nucl. Phys. B 485, 551 (1997).
28. R.M. Ziff, S.R. Finch, V.S. Adamchik, Phys. Rev. Lett. 79, 3447 (1997).
29. S. Galam, A. Mauger, Eur. Phys. J. B 1, 255 (1998).
30. S.C. van der Marck, Int. J. Mod. Phys. C 9, 529 (1998).
31. P. Kleban, R.M. Ziff, Phys. Rev. B 57, R8075 (1998).
32. M. Acharyya, D. Stauffer, Int. J. Mod. Phys. C 9, 643 (1998)
33. J.L. Cardy, J. Phys. A 31, L105 (1998).
34. Chai-Yu Lin, Chin-Kun Hu, Jau-Ann Chen, J. Phys. A 31, L111 (1998).
35. H.K. Janssen, K. Oerding, F. van Wijland, H.J. Hilhorst, Eur. Phys. J. B 7, 137 (1999).
36. A. Bunde, J.W. Kantelhardt, L. Schweitzer, Phys. Rev. Lett. 22, 4907 (1998); J.W. Kantelhardt, A. Bunde, L. Schweitzer, Phys. Rev. Lett. 81, 4907 (1998).
37. A. Bunde, J.W. Kantelhardt, L. Schweitzer, Phys. Rev. Lett. 22, 4907 (1998); J.W. Kantelhardt, A. Bunde, L. Schweitzer, Phys. Rev. Lett. 81, 4907 (1998).
38. R.M. Ziff, C.D. Lorentz, P. Kleban, Physica A 266, 17 (1999).
39. P.N. Suding, R.M. Ziff, Phys. Rev. E 60, 275 (1999).
40. A. Bunde, S. Havlin, M. Porto, Distribution of Dangling Ends on the Incipient Percolation Cluster, 210th WE-Heraeus Seminar on Percolation, Interaction, Simulations of Transport in Disordered Systems, PILS'98 Berlin, Germany; 6 - 9 Oct 1998, Proceedings M Schreiber, Ann. Phys. (Leipzig) 8, 5 (1998).
41. A. Bunde, S. Havlin, M. Porto, H.E. Roman, Phys. Rev. E 58, 5205 (1998).
42. J. Tobochnik, Phys. Rev. E, 5205 (1999).
43. C Moore, Some Polyomono Tilings of the Plane, Santa Fe Institute (1999). Preprint cond-mat/99-04-032 at http://xxx.lanl.gov.
44. L.N. Shchur, 12th Workshop on Computer Simulation Studies in Condensed Matter Physics Athens, GA, USA; Proceedings D.P. Landau et al. (Springer, Berlin, 1999).
45. Y.Y. Tarasevich, S.C. van der Marck, Int. J. Mod. Phys. C 10, 1193 (1999).
46. Y. Lee, J.S. Andrade Jr., S.V. Buldyrev, N.V. Dokholyan, S. Havlin, P.R. King, G. Paul, H.E. Stanley, Phys. Rev. E 60, 3425 (1999).
47. J.J. Normand, H.J. Herrmann, Int. J. Mod. Phys. C 6, 813 (1995).
48. J.J. Normand, H.J. Herrmann, Int. J. Mod. Phys. C 1, 207 (1990).
49. J.J. Normand, H.J. Herrmann, J. Comp. Phys. 64, 380 (1986).
50. S.C. van der Marck, Int. J. Mod. Phys. C 9, 529 (1998).