Percolation thresholds, critical exponents, and scaling functions on planar random lattices and their duals

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 60, Issue 6 A, 1999, Pages 6361-6370

  Hsu, H P ^a,b   Huang, M C ^a  

^a CHUNG YUAN CHRISTIAN UNIVERSITY   (Taiwan)

^b ACADEMIA SINICA   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000318375     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.60.6361     Document Type: Article

References (37)

1. D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd ed. (Taylor and Francis, London, 1992), and references therein.
2. P. J. Reynolds, H. E. Stanley, and W. Klein, Phys. Rev. B 21, 1223 (1980).
3. T. A. Larsson, J. Phys. A 19, 2383 (1986).
4. C. K. Hu and C. N. Chen, Phys. Rev. B 38, 2765 (1988); Phys. Lett. A 130, 436 (1988).
5. C. K. Hu and C. N. Chen, Phys. Rev. B 38, 2765 (1988); Phys. Lett. A 130, 436 (1988).
6. R. M. Ziff, Phys. Rev. Lett. 69, 2670 (1992).
7. P. Grassberger, J. Phys. A 25, 5867 (1992).
8. R. P. Langlands, C. Pichet, Ph. Pouliot, and Y. Saint-Aubin, J. Stat. Phys. 67, 553 (1992).
9. J. L. Cardy, J. Phys. A 25, L201 (1992).
10. U. Gropengiesser and D. Stauffer, Physica A 210, 320 (1994).
11. C.-K. Hu, J. Phys. A 27, L813 (1994).
12. R. P. Langlands, P. Pouliot, and Y. Saint-Aubin, Bull. Am. Math. Soc. 30, 1 (1994).
13. A. Aharony and J.-P. Hovi, Phys. Rev. Lett. 72, 1941 (1994).
14. M. Sahimi and H. Rassamdana, J. Stat. Phys. 78, 1157 (1995).
15. C. K. Hu, C. Y. Lin, and J. A. Chen, Phys. Rev. Lett. 75, 193 (1995).
16. C.-K. Hu, C.-N. Chen, and F.-Y. Wu, J. Stat. Phys. 82, 1199 (1996).
17. J.-P. Hovi and A. Aharony, Phys. Rev. E 53, 235 (1996).
18. R. M. Ziff, Phys. Rev. E 54, 2547 (1996).
19. F. Yonezawa, S. Sakamoto, and M. Hori, Phys. Rev. B 40, 636 (1989); 40, 650 (1989).
20. F. Yonezawa, S. Sakamoto, and M. Hori, Phys. Rev. B 40, 636 (1989); 40, 650 (1989).
21. M. P. M. den Nijs, J. Phys. A 12, 1857 (1979).
22. H. W. J. Blote, M. P. Nightingale, and B. Derrida, J. Phys. A 14, L45 (1981).
23. C. Itzykson and J. M. Drouffe, Statistical Field Theory (Cambridge University Press, Cambridge, 1992), Vol. 2, p. 738.
24. N. H. Christ, R. Friedberg, and T. D. Lee, Nucl. Phys. B 202, 89 (1982).
25. N. H. Christ, R. Friedberg, and T. D. Lee, Nucl. Phys. B 210, 310 (1982); 210, 337 (1982).
26. N. H. Christ, R. Friedberg, and T. D. Lee, Nucl. Phys. B 210, 310 (1982); 210, 337 (1982).
27. J. Hoshen and R. Kopelman, Phys. Rev. B 14, 3438 (1976).
28. p=pc indicate that the contribution from the second kind of percolating path is almost the same as that from the first kind.
29. p=pc indicate that the contribution from the second kind of percolating path is almost the same as that from the first kind.
30. M. E. Fisher, in Proceedings of the 1970 Enrico Fermi Institute School of Physics, edited by M. S. Green (Academic, New York, 1971), Vol. 51, p. 1.
31. M. E. Fisher and M. N. Barber, Phys. Rev. Lett. 28, 1516 (1972).
32. V. Privman and M. E. Fisher, Phys. Rev. B 30, 322 (1984).
33. A. L. Efros, Physics and Geometry of Disorder Percolation Theory (MIR, Moscow, 1986).
34. M. F. Sykes and J. W. Essam, Phys. Rev. Lett. 10, 3 (1963); J. Math. Phys. 5, 1117 (1964).
35. M. F. Sykes and J. W. Essam, Phys. Rev. Lett. 10, 3 (1963); J. Math. Phys. 5, 1117 (1964).
36. H. Kesten, Percolation Theory for Mathematician (Birkhauser, Boston, 1982).
37. H. Scher and R. Zallen, J. Chem. Phys. 53, 3759 (1970).