Journal of Statistical Physics

, Volume 79, Issue 1–2, pp 13–23

Are damage spreading transitions generically in the universality class of directed percolation?

  • Peter Grassberger


We present numerical evidence for the fact that the damage spreading transition in the Domany-Kinzel automaton found by Martinset al. is in the same universality class as directed percolation. We conjecture that also other damage spreading transitions should be in this universality class, unless they coincide with other transitions (as in the Ising model with Glauber dynamics) and provided the probability for a locally damaged state to become healed is not zero.

Key Words

Damage spreading directed percolation stochastic cellular automata critical behavior kinetic second-order phase transitions 


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  1. 1.
    T. M. Liggett,Interacting Particle Systems (Springer, New York, 1985).Google Scholar
  2. 2.
    D. Mollison,J. R. Stat. Soc. B 39:283 (1977).Google Scholar
  3. 3.
    P. Grassberger and K. Sundermeyer,Phys. Lett. B 77:220 (1978).Google Scholar
  4. 4.
    J. Cardy and R. L. Sugar,J. Phys. A,13:L423 (1980).Google Scholar
  5. 5.
    M. Moshe,Phys. Rep. C 37:255 (1978).Google Scholar
  6. 6.
    R. Ziff, E. Gulari, and Y. Barshad,Phys. Rev. Lett. 56:2553 (1986).Google Scholar
  7. 7.
    I. Jensen, H. C. Fogedby, and R. Dickman,Phys. Rev. A 41:3411 (1990).Google Scholar
  8. 8.
    P. Beney, M. Droz, and L. Frachebourg,J. Phys. A 23:3353 (1990).Google Scholar
  9. 9.
    E. V. Albano,Phys. Rev. Lett. 69:656 (1992).Google Scholar
  10. 10.
    I. Jensen, Ph. D. thesis, Aarhus University (1992).Google Scholar
  11. 11.
    J. Zhuo, S. Redner, and H. Park,J. Phys. A 26:4197 (1993).Google Scholar
  12. 12.
    P. Grassberger, unpublished.Google Scholar
  13. 13.
    H. K. Janssen,Z. Phys. B 42:151 (1981).Google Scholar
  14. 14.
    P. Grassberger,Z. Phys. B 47:365 (1982).Google Scholar
  15. 15.
    Y. Pomeau,Physica D 23:3 (1986).Google Scholar
  16. 16.
    P. Grassberger and T. Schreiber,Physica D 50:177 (1991).Google Scholar
  17. 17.
    G. Grinstein, Z. W. Lai, and D. A. Browne,Phys. Rev. A 40:4820 (1989).Google Scholar
  18. 18.
    P. Grassberger, F. Krause, and T. von der, Twer,J. Phys. A 17 L105 (1984); P. Grassberger,J. Phys. A 22:L1103 (1989).Google Scholar
  19. 19.
    H. Takayasu and A. Yu. Tretyakov,Phys. Rev. Lett. 68:3060 (1992).Google Scholar
  20. 20.
    I. Jensen, Melbourne preprint (May 1994).Google Scholar
  21. 21.
    J. Köhler and D. ben-Avraham,J. Phys. A 24:L621 (1991).Google Scholar
  22. 22.
    K. Yaldram, K. M. Khan, N. Ahmed, and M. A. Khan,J. Phys. A 26:L801 (1993).Google Scholar
  23. 23.
    I. Jensen,Phys. Rev. Lett. 70:1465 (1993).Google Scholar
  24. 24.
    I. Jensen, and R. Dickman,Phys. Rev. E 48:1710 (1993).Google Scholar
  25. 25.
    J. F. F. Mendes, R. Dickman, M. Henkel, and M. Ceu Marques,J. Phys. A 27:3019 (1994).Google Scholar
  26. 26.
    I. Jensen, Melbourne preprint (May 1994).Google Scholar
  27. 27.
    H. E. Stanley, D. Stauffer, J. Kertész, and H. Herrmann,Phys. Rev. Lett. 59: 2326 (1987).Google Scholar
  28. 28.
    U. M. S. Costa,J. Phys. A 20:L583 (1987).Google Scholar
  29. 29.
    G. le Caër,Physica A 159:329 (1989).Google Scholar
  30. 30.
    L. de Arcangelis, A. Coniglio, and H. J. Herrmann,Europhys. Lett. 9:749 (1989).Google Scholar
  31. 31.
    I. A. Campbell,Europhys. Lett. 21:9569 (1993).Google Scholar
  32. 32.
    N. Jan and T. S. Ray,J. Stat. Phys. 75:1197 (1994).Google Scholar
  33. 33.
    S. A. Kauffman,J. Theor. Biol. 22:437 (1969).Google Scholar
  34. 34.
    B. Derrida and D. Stauffer,Europhys. Lett. 2:739 (1986).Google Scholar
  35. 35.
    L. R. da Silva and H. J. Herrmann,J. Stat. Phys. 52:463 (1988).Google Scholar
  36. 36.
    A. J. Noest,Phys. Rev. Lett. 57:90 (1986).Google Scholar
  37. 37.
    S. P. Obukhov and D. Stauffer,J. Phys. A 22:1715 (1989).Google Scholar
  38. 38.
    E. Domany and W. Kinzel,Phys. Rev. Lett. 53:447 (1984).Google Scholar
  39. 39.
    J. W. Essam,J Phys. A,22:4927 (1989).Google Scholar
  40. 40.
    W. Kinzel,Z. Phys. B 58:229 (1985).Google Scholar
  41. 41.
    G. A. Kohring and M. Schreckenberg,J. Phys. I (France)2:2033 (1992).Google Scholar
  42. 42.
    F. Bagnoli et al.,J. Phys. A 25:L1071 (1992).Google Scholar
  43. 43.
    M. L. Martins, H. F. Verona de Resende, C. Tsallis, and A. C. N. de Magalhaes,Phys. Rev. Lett. 66:2045.Google Scholar
  44. 44.
    H. Rieger, A. Schadschneider, and M. Schreckenberg,J. Phys. A 27:L423 (1994).Google Scholar
  45. 45.
    R. J. Baxter and A. J. Guttmann,J. Phys. A 21:3193 (1988).Google Scholar
  46. 46.
    J. W. Essam, A. J. Guttmann, and K. de'Bell,J. Phys. A 21:3815 (1988).Google Scholar
  47. 47.
    R. Dickman and I. Jensen,Phys. Rev. Lett. 67:1391 (1991).Google Scholar
  48. 48.
    G. F. Zebende and T. J. P. Penna, preprint (1994).Google Scholar
  49. 49.
    S. V. Buldyrev et al.,Phys. Rev. A 45:R8313 (1992).Google Scholar
  50. 50.
    L. H. Tang and H. Leschhorn,Phys. Rev. Lett. 70:3833 (1993).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Peter Grassberger
    • 1
  1. 1.Physics DepartmentUniversity of WuppertalWuppertalGermany

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