Predictions of bond percolation thresholds for the kagomé and Archimedean (3, 122) lattices

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

Volumn 73, Issue 4, 2006, Pages

  Scullard, Christian R ^a,b   Ziff, Robert M ^b  

^a UNIVERSITY OF CHICAGO   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; PARAMETER ESTIMATION; PERCOLATION (SOLID STATE); PROBLEM SOLVING; SOLID STATE PHYSICS;

APPROXIMATIONS; ARCHIMEDEAN (3, 122) LATTICES; BOND PERCOLATION; KAGOME LATTICES;

LATTICE VIBRATIONS;

EID: 33646391963     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.73.045102     Document Type: Article

References (26)

1. G. Grimmett, Percolation, 2nd ed. (Springer-Verlag, Berlin, 1999).
2. D. Stauffer and A. Aharony, 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, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.016134 73, 016134 (2006).
5. C. R. Scullard, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.016107 73, 016107 (2006).
6. B. Grünbaum and G. C. Shephard, Tilings and Patterns (Freeman, New York, 1987).
7. P. N. Suding and R. M. Ziff, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.275 60, 275 (1999).
8. R. Parviainen, Ph.D. thesis, Uppsala University, Sweden, 2004 (URL http://publications.uu.se/theses/abstract.xsql?dbid=4251).
9. M. F. Sykes and J. W. Essam, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704215 5, 1117 (1964).
10. F. Y. Wu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.090602 96, 090602 (2006).
11. C. Tsallis, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/15/23/007 15, L757 (1982).
12. N. C. Chao, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/21/21/003 21, L741 (1988).
13. M. Hori and K. Kitahara, Percolation thresholds for honeycomb, kagome and triangular lattices, URL http://www.physics.iisc.ernet.in/~statphys22/.
14. F. Y. Wu, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.54.235 54, 235 (1982).
15. F. Y. Wu, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/12/17/002 12, L645 (1979).
16. C. M. Fortuin and P. W. Kasteleyn, Physica (Amsterdam) PHYSAG 0031-8914 57, 636 (1972).
17. C. Tsallis, Physica A PHYADX 0378-4371 10.1016/j.physa.2004.06.054 344, 718 (2004).
18. R. M. Ziff and P. N. Suding, J. Phys. A JPHAC5 0305-4470 15, 5351 (1997).
19. J. C. Wierman, Combinatorics, Probab. Comput. CPCOFG 0963-5483 10.1017/S0963548302005370 12, 95 (2003).
20. W. D. May and J. C. Wierman, Combinatorics, Probab. Comput. CPCOFG 0963-5483 10.1017/S0963548305006802 14, 549 (2005).
21. Y. Y. Tarasevich and S. C. van der Marck, Int. J. Mod. Phys. C IJMPEO 0129-1831 10.1142/S0129183199000978 10, 1193 (1999).
22. K. S. Mendelson, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.6496 60, 6496 (1999).
23. S.-C. Chang and R. Shrock, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.056130 70, 056130 (2004).
24. J. L. Monroe, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.017103 67, 017103 (2003).
25. I. Jensen, A. J. Guttmann, and I. G. Enting, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/30/23/008 30, 8067 (1997).
26. W. D. May and J. C. Wierman (private communication).