An infinite number of effectively infinite clusters in critical percolation

Journal of Statistical Physics

Volumn 92, Issue 1-2, 1998, Pages 325-330

  Jan, Naeem ^c   Stauffer, Dietrich ^a,b   Aharony, Amnon ^a  

^a TEL AVIV UNIVERSITY   (Israel)

^b UNIVERSITY OF COLOGNE   (Germany)

^c NONE

Author keywords

Infinite clusters; Percolation; Ranking; Size distribution

Indexed keywords

EID: 0032120986     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1023008021962     Document Type: Article

References (23)

1. A. Margolina and H. J. Herrmann, Phys. Lett. 104A:295 (1984).
2. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1994); A. Bunde and S. Havlin, Fractals and Disordered Systems (Springer, Berlin/Heidelberg, 1996); M. Sahimi, Applications of Percolation Theory (Taylor and Francis, London, 1994).
3. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1994); A. Bunde and S. Havlin, Fractals and Disordered Systems (Springer, Berlin/Heidelberg, 1996); M. Sahimi, Applications of Percolation Theory (Taylor and Francis, London, 1994).
4. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1994); A. Bunde and S. Havlin, Fractals and Disordered Systems (Springer, Berlin/Heidelberg, 1996); M. Sahimi, Applications of Percolation Theory (Taylor and Francis, London, 1994).
5. S. MacLeod and N. Jan, Int. J. Mod. Phys. C 9:289 (1998); for three dimensions see N. Jan and D. Stauffer, 9:349 (1998).
6. S. MacLeod and N. Jan, Int. J. Mod. Phys. C 9:289 (1998); for three dimensions see N. Jan and D. Stauffer, 9:349 (1998).
7. M. Aizenman, H. Kesten, and C. M. Newman, Comm. Math. Phys. 111:505 (1987); R. M. Burton and M. Keane, Comm. Math. Phys. 121:501 (1989); A. Gandolfi, G. R. Grimmett, and L. Russo, Comm. Math. Phys. 114 (1988); see also C. M. Newman and L. S. Schulman, J. Stat. Phys. 26:613 (1981).
8. M. Aizenman, H. Kesten, and C. M. Newman, Comm. Math. Phys. 111:505 (1987); R. M. Burton and M. Keane, Comm. Math. Phys. 121:501 (1989); A. Gandolfi, G. R. Grimmett, and L. Russo, Comm. Math. Phys. 114 (1988); see also C. M. Newman and L. S. Schulman, J. Stat. Phys. 26:613 (1981).
9. M. Aizenman, H. Kesten, and C. M. Newman, Comm. Math. Phys. 111:505 (1987); R. M. Burton and M. Keane, Comm. Math. Phys. 121:501 (1989); A. Gandolfi, G. R. Grimmett, and L. Russo, Comm. Math. Phys. 114 (1988); see also C. M. Newman and L. S. Schulman, J. Stat. Phys. 26:613 (1981).
10. M. Aizenman, H. Kesten, and C. M. Newman, Comm. Math. Phys. 111:505 (1987); R. M. Burton and M. Keane, Comm. Math. Phys. 121:501 (1989); A. Gandolfi, G. R. Grimmett, and L. Russo, Comm. Math. Phys. 114 (1988); see also C. M. Newman and L. S. Schulman, J. Stat. Phys. 26:613 (1981).
11. M. Aizenman, in STATPHYS 19, Proceedings Xiamen 1995, H. Bai-lin, ed. (World Scientific, Singapore, 1995), and Nucl. Phys. (FS)B 485:551 (1997).
12. M. Aizenman, in STATPHYS 19, Proceedings Xiamen 1995, H. Bai-lin, ed. (World Scientific, Singapore, 1995), and Nucl. Phys. (FS)B 485:551 (1997).
13. L. de Arcangelis, J. Phys. A 20:3057 (1987): C. K. Hu and C. -Y. Lin, Phys. Rev. Lett. 77:8 (1996): P. Sen, Int. J. Mod. Phys. C 7:603 (1996). 8:229 (1997); L. N. Shchur and S. S. Kosyakov, Int. J. Mod. Phys. C 8:473 (1997); D. Stauffer, Physica A 242:1 (1997).
14. L. de Arcangelis, J. Phys. A 20:3057 (1987): C. K. Hu and C. -Y. Lin, Phys. Rev. Lett. 77:8 (1996): P. Sen, Int. J. Mod. Phys. C 7:603 (1996). 8:229 (1997); L. N. Shchur and S. S. Kosyakov, Int. J. Mod. Phys. C 8:473 (1997); D. Stauffer, Physica A 242:1 (1997).
15. L. de Arcangelis, J. Phys. A 20:3057 (1987): C. K. Hu and C. -Y. Lin, Phys. Rev. Lett. 77:8 (1996): P. Sen, Int. J. Mod. Phys. C 7:603 (1996). 8:229 (1997); L. N. Shchur and S. S. Kosyakov, Int. J. Mod. Phys. C 8:473 (1997); D. Stauffer, Physica A 242:1 (1997).
16. L. de Arcangelis, J. Phys. A 20:3057 (1987): C. K. Hu and C. -Y. Lin, Phys. Rev. Lett. 77:8 (1996): P. Sen, Int. J. Mod. Phys. C 7:603 (1996). 8:229 (1997); L. N. Shchur and S. S. Kosyakov, Int. J. Mod. Phys. C 8:473 (1997); D. Stauffer, Physica A 242:1 (1997).
17. L. de Arcangelis, J. Phys. A 20:3057 (1987): C. K. Hu and C. -Y. Lin, Phys. Rev. Lett. 77:8 (1996): P. Sen, Int. J. Mod. Phys. C 7:603 (1996). 8:229 (1997); L. N. Shchur and S. S. Kosyakov, Int. J. Mod. Phys. C 8:473 (1997); D. Stauffer, Physica A 242:1 (1997).
18. L. de Arcangelis, J. Phys. A 20:3057 (1987): C. K. Hu and C. -Y. Lin, Phys. Rev. Lett. 77:8 (1996): P. Sen, Int. J. Mod. Phys. C 7:603 (1996). 8:229 (1997); L. N. Shchur and S. S. Kosyakov, Int. J. Mod. Phys. C 8:473 (1997); D. Stauffer, Physica A 242:1 (1997).
19. A. Margolina, H. J. Herrmann, and D. Stauffer, Phys. Lett. 93A:73 (1982).
20. M. S. Watanabe. Phys. Rev. E 53:4187 (1996) and 54:5583 (erratum, 1996).
21. M. S. Watanabe. Phys. Rev. E 53:4187 (1996) and 54:5583 (erratum, 1996).
22. B. B. Mandelbrot, Fractals and Scaling in Finance (Springer, New York, 1997), p. 113.
23. K. Binder and D. Stauffer, Applications of the Monte Carlo Method in Statistical Physics, K. Binder, ed. (Springer Verlag, Berlin/Heidelberg. 1984), Chap. 8. p. 241.