Renormalization group calculation of distribution functions: Structural properties for percolation clusters

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

Volumn 56, Issue 1 SUPPL. A, 1997, Pages 172-184

  Hovi, J P ^a,b   Aharony, Amnon ^a,c  

^a TEL AVIV UNIVERSITY   (Israel)

^b AALTO UNIVERSITY   (Finland)

^c UNIVERSITY OF OSLO   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001165019     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.56.172     Document Type: Article

References (44)

1. A. B. Harris and A. Aharony, Europhys. Lett. 4, 1355 (1987).
2. A. Bunde, H. E. Roman, S. Russ, A. Aharony, and A. B. Harris, Phys. Rev. Lett. 69, 3189 (1992).
3. A. Aharony, Y. Gefen, and Y. Kantor, J. Stat. Phys. 36, 795 (1984).
4. B. B. Mandelbrot and J. A. Given, Phys. Rev. Lett. 52, 1853 (1984).
5. D. Stauffer and A. Aharony, Introduction to Percolation Theory, revised 2nd ed. (Taylor and Francis, London, 1994).
6. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Fransisco. 1982).
7. A. Kapitulnik, A. Aharony, G. Deutscher, and D. Stauffer, J. Phys. A 16, L269 (1984).
8. J.-P. Hovi, A. Aharony, D. Stauffer, and B. B. Mandelbrot, Phys. Rev. Lett. 77, 877 (1996).
9. S. Havlin and R. Nossal, J. Phys. A 17, L427 (1984).
10. S. Havlin, B. L. Trus, G. H. Weiss, and D. Ben-Avraham, J. Phys. A 18, L247 (1985).
11. A. U. Neumann and S. Havlin, J. Stat. Phys. 52, 203 (1988).
12. D. Lhuiller, J. Phys. (France) 49, 705 (1988).
13. A. K. Roy and A. Blumen, J. Stat. Phys. 59, 1581 (1990).
14. P. J. Reynolds, H. E. Stanley, and W. Klein, J. Phys. C 10, L167 (1977).
15. J. Bernasconi, Phys. Rev. B 18, 2185 (1978).
16. A. Aharony, E. I. Hinrichsen, A. Hansen, J. Feder, T. Jøssang, and H. H. Hardy, Physica A 177, 260 (1991).
17. J.-P. Hovi and A. Aharony, Fractals 3, 453 (1995).
18. P. Le Doussal and J. Machta, J. Stat. Phys. 64, 541 (1991).
19. J.-P. Hovi and A. Aharony, J. Stat. Phys. 86, 1163 (1997).
20. D. C. Hong and H. E. Stanley, J. Phys. A 16, L475 (1983).
21. A. Coniglio, Phys. Rev. Lett. 46, 250 (1981).
22. H. J. Herrmann and H. E. Stanley, J. Phys. A 21, L879 (1988).
23. K. Y. Woo and S. B. Lee, Phys. Rev. A 44, 999 (1991).
24. P. Grassberger, J. Phys. A 26, 1023 (1993).
25. M. D. Rintoul, J. Moon, and H. Nakanishi, Phys. Rev. E 49, 2790 (1994).
26. P. Grassberger, J. Phys. A 25, 5475 (1992).
27. T. E. Harris, The Theory of Branching Processes (Springer, Berlin, 1963); K. B. Athreya and P. E. Ney, Branching Processes (Springer, Berlin, 1972).
28. T. E. Harris, The Theory of Branching Processes (Springer, Berlin, 1963); K. B. Athreya and P. E. Ney, Branching Processes (Springer, Berlin, 1972).
29. H. W. Watson and F. Galton, J. Anthropol. Inst. Great Britain Ireland 4, 138 (1874).
30. T. E. Harris, Ann. Math. Stat. , 41, 474 (1948).
31. N. H. Bingham, J. Appl. Probab. 25A, 215 (1988).
32. J. D. Biggins and N. H. Bingham, Adv. Appl. Probab. 25, 757 (1993).
33. S. Dubuc, Z. Wahrscheinlichkeitstheor. Verwandte Geb. 19, 281 (1971).
34. J. D. Biggins and N. H. Bingham, Math. Proc. Camb. Philos. Soc. Soc. 110, 545 (1991).
35. The periodic functions of Theorems 1 and 2 are completely determined by f [29]. Thus, their determination in the small cell RG calculations does not involve any fitting of the data.
36. The correction terms to the exponential decay, form an active mathematical problem in it's own right. [J. D. Biggins and N. H. Bingham (private communication).]
37. A. Aharony and A. B. Harris, Physica A 191, 365 (1992).
38. (1/dmin). Assuming that the leading exponential terms are the same as for fixed Euclidean distance, the data shown in Fig. 7 are calculated by changing variables.
39. Y. Kantor, J. Phys. A 19, L497 (1986).
40. M. Aizenman, Nucl. Phys. B 445, 551 (1997).
41. A. M. Yaglom, Doklady 56, 795 (1947).
42. R. S. Slack, Z. Wahrscheinlichkeitstheor. Verwandte Geb. 9, 139 (1968).
43. P. Sen, Int. J. Mod. Phys. 7, 603 (1996).
44. C. K. Hu and C. Y. Lin, Phys. Rev. Lett. 77, 8 (1996).