Percolation on hyperbolic lattices

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

Volumn 79, Issue 1, 2009, Pages

  Baek, Seung Ki ^a   Minnhagen, Petter ^a   Kim, Beom Jun ^b  

^a UMEÅ UNIVERSITY   (Sweden)

^b Sungkyunkwan University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

PERCOLATION (SOLID STATE); SOLVENTS;

CAYLEY TREES; CRITICAL EXPONENTS; FINITE FRACTIONS; FINITE-SIZE SCALING; FINITE-SIZE SCALING METHODS; PERCOLATION THRESHOLDS; PERCOLATION TRANSITIONS; UNIVERSALITY CLASS;

PERCOLATION (FLUIDS);

EID: 60449097530     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.011124     Document Type: Article

References (33)

1. S. N. Dorogovtsev and A. V. Goltsev, Rev. Mod. Phys. 80, 1275 (2008). 10.1103/RevModPhys.80.1275
2. Y. Gefen, B. B. Mandelbrot, and A. Aharony, Phys. Rev. Lett. 45, 855 (1980); 10.1103/PhysRevLett.45.855
3. S. Havlin, D. ben-Avraham, and D. Movshovitz, Phys. Rev. Lett. 51, 2347 (1983); 10.1103/PhysRevLett.51.2347
4. B. Kutnjak-Urbanc, S. Zapperi, S. Milošević, and H. E. Stanley, Phys. Rev. E 54, 272 (1996); 10.1103/PhysRevE.54.272
5. H. D. Rozenfeld and D. ben-Avraham, Phys. Rev. E 75, 061102 (2007). 10.1103/PhysRevE.75.061102
6. J. S. Andrade, H. J. Herrmann, R. F. S. Andrade, and L. R. da Silva, Phys. Rev. Lett. 94, 018702 (2005). 10.1103/PhysRevLett.94.018702
7. H. Shima and Y. Sakaniwa, J. Stat. Mech.: Theory Exp. (2006) P08017; 10.1088/1742-5468/2006/08/P08017
8. H. Shima and Y. Sakaniwa, J. Phys. A 39, 4921 (2006); 10.1088/0305-4470/39/18/010
9. S. K. Baek, P. Minnhagen, and B. J. Kim, Europhys. Lett. 79, 26002 (2007); 10.1209/0295-5075/79/26002
10. S. K. Baek, S. D. Yi, and B. J. Kim, Phys. Rev. E 77, 022104 (2008); 10.1103/PhysRevE.77.022104
11. C. D. Modes and R. D. Kamien, Phys. Rev. Lett. 99, 235701 (2007). 10.1103/PhysRevLett.99.235701
12. D. Vanderbilt and J. Tersoff, Phys. Rev. Lett. 68, 511 (1992); 10.1103/PhysRevLett.68.511
13. N. Park, M. Yoon, S. Berber, J. Ihm, E. Osawa, and D. Tománek, Phys. Rev. Lett. 91, 237204 (2003). 10.1103/PhysRevLett.91.237204
14. R. H. Schonmann, in Perplexing Probability Problems: Papers in Honor of Harry Kesten, edited by, M. Bramson, and, R. Durrett, (Birkhäuser, Boston, 1999), pp. 53-67.
15. I. Benjamini, R. Lyons, Y. Peres, and O. Schramm, Ann. Probab. 27, 1347 (1999); 10.1214/aop/1022677450
16. I. Benjamini and O. Schramm, J. Am. Math. Soc. 14, 487 (2001). 10.1090/S0894-0347-00-00362-3
17. R. Lyons, J. Math. Phys. 41, 1099 (2000). 10.1063/1.533179
18. D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd ed. (Taylor & Francis, London, 2003).
19. R. H. Schonmann, Commun. Math. Phys. 219, 271 (2001); 10.1007/s002200100417
20. R. H. Schonmann, Commun. Math. Phys. 225, 453 (2002). 10.1007/s002200100587
21. M. E. J. Newman and R. M. Ziff, Phys. Rev. Lett. 85, 4104 (2000); 10.1103/PhysRevLett.85.4104
22. M. E. J. Newman and R. M. Ziff, Phys. Rev. E 64, 016706 (2001). 10.1103/PhysRevE.64.016706
23. A. Zen, A. KabakçIoǧlu, and A. L. Stella, Phys. Rev. E 76, 026110 (2007). 10.1103/PhysRevE.76.026110
24. B. Sapoval, M. Rosso, and J. F. Gouyet, J. Phys. (France) Lett. 46, L149 (1985).
25. S. K. Baek, P. Minnhagen, and B. J. Kim (unpublished).
26. H. S. M. Coxeter, M. S. Longuet-Higgins, and J. C. P. Miller, Philos. Trans. R. Soc. London, Ser. A 246, 401 (1954). 10.1098/rsta.1954.0003
27. H. S. M. Coxeter, Can. Math. Bull. 40, 158 (1997).
28. J. W. Anderson, Hyperbolic Geometry (Springer, London, 1999).
29. B. Söderberg, Phys. Rev. E 47, 4582 (1993). 10.1103/PhysRevE.47.4582
30. P. J. Flory, J. Am. Chem. Soc. 63, 3083 (1941). 10.1021/ja01856a061
31. G. Grimmett, Percolation (Springer, New York, 1989).
32. S. K. Baek, Hoang Anh Tuan Kiet, and B. J. Kim, Phys. Rev. E 76, 046113 (2007). 10.1103/PhysRevE.76.046113
33. A. G. Hunt, Percolation Theory for Flow in Porous Media (Springer, Berlin, 2005).