Exact site percolation thresholds using a site-to-bond transformation and the star-triangle transformation

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 73, Issue 1, 2006, Pages

  Scullard, Christian R ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION METHODS; CRYSTAL LATTICES; MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING;

EXACT SITE PERCOLATION THRESHOLDS; HEXAGONAL LATTICE; SITE-TO-BOND TRANSFORMATION;

PERCOLATION (FLUIDS);

EID: 32844474582     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.73.016107     Document Type: Article

References (14)

1. G. Grimmett, Percolation, 2nd ed. (Springer-Verlag, Berlin, 1999).
2. D. Stauffer, Introduction to Percolation Theory, 2nd ed. (Taylor and Francis, London, 1991).
3. S. R. Broadbent and J. M. Hammersley, Proc. Cambridge Philos. Soc. PCPSA4 0068-6735 53, 629 (1957).
4. R. M. Ziff and P. N. Suding, J. Phys. A JPHAC5 0305-4470 15, 5351 (1997).
5. M. F. Sykes and J. W. Essam, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704215 5, 1117 (1964).
6. J. C. Wierman, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/17/7/020 17, 1525 (1984).
7. H. Kesten, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01197577 74, 41 (1980).
8. J. C. Wierman, J. Phys. A JPHAC5 0305-4470 15, 5351 (1981).
9. B. Grünbaum and G. C. Shephard, Tilings and Patterns (Freeman, New York, 1987).
10. S. R. Finch, Mathematical Constants (Cambridge University Press, Cambridge, 2003).
11. R. M. Ziff, Phys. Rev. E (to be published).
12. P. N. Suding and R. M. Ziff, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.275 60, 275 (1999).
13. I. Kondor, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/13/22/001 13, L531 (1980).
14. Z. V. Djordjevic, H. E. Stanley, and A. Margolina, J. Phys. A JPHAC5 0305-4470 30, L405 (1982).