Dynamical real space renormalization group applied to sandpile models

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

Volumn 60, Issue 2, 1999, Pages 1239-1251

  Ivashkevich, Eugene V ^a   Povolotsky, Alexander M ^a   Vespignani, Alessandro ^b   Zapperi, Stefano ^c  

^a JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

^b ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

^c ESPCI   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000129056     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.1239     Document Type: Article

References (44)

1. Phase Transition and Critical Phenomena, edited by C. Domb and M. S. Green (Academic Press, London, 1972–1976), Vols. 1–6;Phase Transition and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, London, 1983–1995), Vols. 7–17.
2. S. Katz, J.L. Lebowitz, and H. Spohn, Phys. Rev. B 28, 1655 (1983)
3. S. KatzJ.L. LebowitzH. SpohnJ. Stat. Phys. 34, 497 (1984).
4. B. Schmittmann and R. K. Zia, in Phase Transition and Critical Phenomena (Ref. 1), Vol. 17.
5. T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1992).
6. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman and Company, New York, 1983).
7. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)
8. P. BakC. TangK. WiesenfeldPhys. Rev. A 38, 364 (1988).
9. For a review, see, e.g., P. Bak and M. Creutz, in Fractals and Disordered Systems, edited by A. Bunde and S. Havlin (Springer-Verlag, Heidelberg, 1993), Vol. II; G. Grinstein, in Scale Invariance, Interfaces and Non-Equilibrium Dynamics, edited by A. McKane et al., Vol. 344 of NATO Advanced Study Institute, Series B: Physics (Plenum, New York, 1995).
10. P. Bak, K. Chen, and C. Tang, Phys. Lett. A 147, 297 (1990).
11. B. Drossel and F. Schwabl, Phys. Rev. Lett. 69, 1629 (1992).
12. A. Vespignani and S. Zapperi, Phys. Rev. Lett. 78, 4793 (1997)
13. A. VespignaniS. ZapperiPhys. Rev. E 57, 6345 (1998)
14. Phys. Rev. ER. Dickman, A. Vespignani, and S. Zapperi, 57, 5095 (1998).
15. L. Pietronero, A. Vespignani, and S. Zapperi, Phys. Rev. Lett. 72, 1690 (1994)
16. A. Vespignani, S. Zapperi, and L. Pietronero, Phys. Rev. E 51, 1711 (1995).
17. V. Loreto, L. Pietronero, A. Vespignani, and S. Zapperi, Phys. Rev. Lett. 75, 465 (1995).
18. A. Vespignani, S. Zapperi, and V. Loreto, Phys. Rev. Lett. 77, 4560 (1996)
19. A. VespignaniS. ZapperiV. LoretoJ. Stat. Phys. 88, 47 (1997).
20. E.V. Ivashkevich, Phys. Rev. Lett. 76, 3368 (1996).
21. J. Hasty and K. Wiesenfeld, J. Stat. Phys. 86, 1179 (1997).
22. A. Ben-Hur, R. Hallgass, and V. Loreto, Phys. Rev. E 54, 1426 (1996).
23. J. Hasty and K. Wiesenfeld, Phys. Rev. Lett. 81, 1722 (1998).
24. T. Tomé and M.J. de Oliveira, Phys. Rev. E 55, 4000 (1997)
25. Phys. Rev. EM.J. de Oliveira and J.E. Satulovsky, 55, 6377 (1997).
26. Y.C. Zhang, Phys. Rev. Lett. 63, 470 (1989)
27. L. Pietronero, P. Tartaglia, and Y. C. Zhang, Physica A 173, 129 (1991).
28. S.S. Manna, J. Phys. A 24, L363 (1991).
29. P. Grassberger and S.S. Manna, J. Phys. (France) 51, 1077 (1990).
30. A.L. Stella, C. Tebaldi, and G. Caldarelli, Phys. Rev. E 52, 72 (1995).
31. S. Lübeck and K.D. Usadel, Phys. Rev. E 55, 4095 (1997)
32. Phys. Rev. ES. Lübeck, 56, 1590 (1997).
33. D. Dhar, Phys. Rev. Lett. 64, 1613 (1990).
34. S.N. Majumdar and D. Dhar, J. Phys. A 24, L357 (1991).
35. V.B. Priezzhev, J. Stat. Phys. 74, 955 (1994).
36. E.V. Ivashkevich, J. Phys. A 27, 3643 (1994).
37. E.V. Ivashkevich, D.V. Ktitarev, and V.B. Priezzhev, J. Phys. A 27, L585 (1994).
38. V.B. Priezzhev, D.V. Ktitarev, and E.V. Ivashkevich, Physica A 209, 347 (1994).
39. V.B. Priezzhev, D.V. Ktitarev, and E.V. Ivashkevich, Phys. Rev. Lett. 76, 2093 (1996).
40. T. Niemeijer and J.M.J. van Leeuwen, in Phase Transition and Critical Phenomena (Ref. 1), Vol. 6.
41. R. Dickman, Phys. Rev. A 38, 2588 (1988).
42. A. Ben-Hur and O. Biham, Phys. Rev. E 53, R1317 (1996)
43. Phys. Rev. EE. Milshtein, O. Biham, and S. Solomon, 58, 303 (1998).
44. J.L. Cardy, in Phase Transition and Critical Phenomena (Ref. 1), Vol. 11.