Where two fractals meet: The scaling of a self-avoiding walk on a percolation cluster

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

Volumn 70, Issue 3 2, 2004, Pages

  Von Ferber, C ^a,b   Blavats'ka, V ^c   Folk, R ^b   Holovatch, Yu ^b,d  

^a UNIVERSITY OF FREIBURG   (Germany)

^b JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^c INSTITUTE FOR CONDENSED MATTER PHYSICS   (Ukraine)

^d IVAN FRANKO NATIONAL UNIVERSITY OF LVIV   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTAL LATTICES; FRACTALS; MONTE CARLO METHODS; ORGANIC POLYMERS; PERTURBATION TECHNIQUES; PROBLEM SOLVING; SWELLING;

PERCOLATION CLUSTER; RANDOM RESISTOR NETWORKS (RRN); RANDOM WALK; SELF AVOIDING WALK (SAW);

PERCOLATION (SOLID STATE);

EID: 42749102551     PISSN: 15393755     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.70.035104     Document Type: Article

References (56)

1. P.-G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca and London, 1979).
2. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1992).
3. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1983).
4. H. E. Stanley et al., Physica A 266, 5 (1999).
5. H. Kleinen, J. Neu, V. Schulte-Frohlinde, K. G. Chetyrkin, and S. A. Larin, Phys. Lett. B 272, 39 (1991), Erratum: 319, 545 (1993).
6. A. B. Harris, Z. Phys. B: Condens. Matter 49, 347 (1983); J. W. Lyklema and K. Kremer, ibid. 55, 41 (1984).
7. A. B. Harris, Z. Phys. B: Condens. Matter 49, 347 (1983); J. W. Lyklema and K. Kremer, ibid. 55, 41 (1984).
8. Y. Kim, J. Phys. C 16, 1345 (1983).
9. For a review see, e.g., K. Barat and B. K. Chakrabarti, Phys. Rep. 258, 378 (1995).
10. K. Kremer, Z. Phys. B: Condens. Matter 45, 149 (1981).
11. S. B. Lee and H. Nakanishi, Phys. Rev. Lett. 61, 2022 (1988).
12. S. B. Lee, H. Nakanishi, and Y. Kim, Phys. Rev. B 39, 9561 (1989).
13. K. Y. Woo and S. B. Lee, Phys. Rev. A 44, 999 (1991).
14. P. Grassberger, J. Phys. A 26, 1023 (1993).
15. S. B. Lee, J. Korean Phys. Soc. 29, 1 (1996).
16. Y. Meir and A. B. Harris, Phys. Rev. Lett. 63, 2819 (1989).
17. P. M. Lam, J. Phys. A 23, L831 (1990).
18. H. Nakanishi and J. Moon, Physica A 191, 309 (1992).
19. C. Vanderzande and A. Komoda, Phys. Rev. A 45, R5335 (1992).
20. M. D. Rintoul, J. Moon, and H. Nakanishi, Phys. Rev. E 49, 2790 (1994).
21. A. Ordemann, M. Porto, H. E. Roman, S. Havlin, and A. Bunde, Phys. Rev. E 61, 6858 (2000).
22. H. Nakanishi and S. B. Lee, J. Phys. A 24, 1355 (1991).
23. M. Sahimi, J. Phys. A 17, L379 (1984).
24. R. Rammal, G. Toulouse, and J. Vannimenus, J. Phys. (France) 45, 389 (1984).
25. Y. Kim, J. Phys. A 20, 1293 (1987).
26. A. K. Roy and B. K. Chakrabarti, J. Phys. A 20, 215 (1987).
27. A. Aharony and A. B. Harris, J. Stat. Phys. 54, 1091 (1989).
28. Y. Kim, Phys. Rev. A 41, 4554 (1990).
29. A. K. Roy and A. Blumen, J. Stat. Phys. 59, 1581 (1990).
30. Y. Kim, Phys. Rev, A 45, 6103 (1992).
31. P. M. Lam and Z. Q. Zhang, Z. Phys. B: Condens. Matter 56, 155 (1984).
32. B. Nienhuis, Phys. Rev. Lett. 49, 1062 (1982).
33. R. Guida and J. Zinn-Justin, J. Phys. A 31, 8103 (1998).
34. Apart from logarithmic corrections at d=6, see: H. K. Janssen and O. Stenull, Phys. Rev. E 68, 036131 (2003).
35. A. K. Roy and B. K. Chakrabarti, Phys. Lett. 91A, 393 (1982).
36. P. Le Doussal and J. Machta, J. Stat. Phys. 64, 541 (1991).
37. H. G. E. Hentschel and I. Procaccia, Physica D 8, 435 (1983); T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, B. I. Shraiman et al., Phys. Rev. A 33, 1141 (1986).
38. H. G. E. Hentschel and I. Procaccia, Physica D 8, 435 (1983); T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, B. I. Shraiman et al., Phys. Rev. A 33, 1141 (1986).
39. M. E. Cates and T. A. Witten, Phys. Rev. A 35, 1809 (1987); C. von Ferber and Yu. Holovatch, Phys. Rev. E 59, 6914 (1999); ibid. 65, 042801 (2002).
40. M. E. Cates and T. A. Witten, Phys. Rev. A 35, 1809 (1987); C. von Ferber and Yu. Holovatch, Phys. Rev. E 59, 6914 (1999); ibid. 65, 042801 (2002).
41. M. E. Cates and T. A. Witten, Phys. Rev. A 35, 1809 (1987); C. von Ferber and Yu. Holovatch, Phys. Rev. E 59, 6914 (1999); ibid. 65, 042801 (2002).
42. O. Stenull, H. K. Janssen, Europhys. Lett. 51, 539 (2000); Phys. Rev. E 63, 036103 (2001).
43. O. Stenull, H. K. Janssen, Europhys. Lett. 51, 539 (2000); Phys. Rev. E 63, 036103 (2001).
44. B. Duplantier, Phys. Rev. Lett. 82, 880 (1999).
45. B. Derrida, Phys. Rep. 103, 29 (1984).
46. G. 't Hooft and M. Veltman, Nucl. Phys. B 44, 189 (1972); G. 't Hooft, ibid. 61, 455 (1973).
47. G. 't Hooft and M. Veltman, Nucl. Phys. B 44, 189 (1972); G. 't Hooft, ibid. 61, 455 (1973).
48. D. J. Amit, J. Phys. A 9, 1441 (1976); R. G. Priest and T. C. Lubensky, Phys. Rev. B 13, 4159 (1976); Erratum; 14, 5125(E) (1976).
49. D. J. Amit, J. Phys. A 9, 1441 (1976); R. G. Priest and T. C. Lubensky, Phys. Rev. B 13, 4159 (1976); Erratum; 14, 5125(E) (1976).
50. C. von Ferber, V. Blavats'ka, R. Folk, and Yu. Holovatch, in Statistics of Linear Polymers in Random Media, edited by B. K. Chakrabarti, (Elsevier, Amsterdam, to be published).
51. B. Nienhuis, J. Phys, A 15, 199 (1982); P. N. Strenski, Phys. Rev. Lett. 66, 1330 (1991); N. Jan, D. C. Hong, and H. E. Stanley, J. Phys. A 18, L935 (1985).
52. B. Nienhuis, J. Phys, A 15, 199 (1982); P. N. Strenski, Phys. Rev. Lett. 66, 1330 (1991); N. Jan, D. C. Hong, and H. E. Stanley, J. Phys. A 18, L935 (1985).
53. B. Nienhuis, J. Phys, A 15, 199 (1982); P. N. Strenski, Phys. Rev. Lett. 66, 1330 (1991); N. Jan, D. C. Hong, and H. E. Stanley, J. Phys. A 18, L935 (1985).
54. H. K. Janssen, Z. Phys. B: Condens. Matter 58, 311 (1985); J. Cardy and P. Grassberger, J. Phys. A 18, L267 (1985); H. K. Janssen and O. Stenull, Phys. Rev. E 61, 4821 (2000).
55. H. K. Janssen, Z. Phys. B: Condens. Matter 58, 311 (1985); J. Cardy and P. Grassberger, J. Phys. A 18, L267 (1985); H. K. Janssen and O. Stenull, Phys. Rev. E 61, 4821 (2000).
56. H. K. Janssen, Z. Phys. B: Condens. Matter 58, 311 (1985); J. Cardy and P. Grassberger, J. Phys. A 18, L267 (1985); H. K. Janssen and O. Stenull, Phys. Rev. E 61, 4821 (2000).