Skip to main content
SpringerLink
Log in

Time-dependent perturbation theory for nonequilibrium lattice models

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We develop a time-dependent perturbation theory for nonequilibrium interacting particle systems. We focus on models such as the contact process which evolve via destruction and autocatalytic creation of particles. At a critical value of the destruction rate there is a continuous phase transition between an active steady state and the vacuum state, which is absorbing. We present several methods for deriving series for the evolution starting from a single seed particle, including expansions for the ultimate survival probability in the super- and subcritical regions, expansions for the average number of particles in the subcritical region, and short-time expansions. Algorithms for computer generation of the various expansions are presented. Rather long series (24 terms or more) and precise estimates of critical parameters are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Nicolis and I. Prigogine,Self-Organization in Nonequilibrium Systems (Wiley-Interscience, New York, 1977).

    Google Scholar 

  2. H. Haken,Synergetics (Springer-Verlag, New York, 1983).

    Google Scholar 

  3. P. Grassberger and A. de la Torre,Ann. Phys. (NY)122:373 (1979).

    Google Scholar 

  4. P. Grassberger,J. Phys. A 22:3673 (1989).

    Google Scholar 

  5. R. M. Ziff, E. Gulari, and Y. Barshad,Phys. Rev. Lett. 56:2553 (1986).

    Google Scholar 

  6. I. Jensen, H. C. Fogedby, and R. Dickman,Phys. Rev. A 41:3411 (1990).

    Google Scholar 

  7. R. Dickman,Phys. Rev. B 40:7005 (1989).

    Google Scholar 

  8. R. Dickman,Phys. Rev. A 42:6985 (1990).

    Google Scholar 

  9. T. Aukrust, D. A. Browne, and I. Webman,Phys. Rev. A 41:5294 (1990).

    Google Scholar 

  10. I. Jensen,Phys. Rev. A 43:3187 (1991).

    Google Scholar 

  11. R. Dickman,Phys. Rev. A 34:4246 (1986).

    Google Scholar 

  12. R. Dickman,Phys. Rev. A 38:2588 (1988).

    Google Scholar 

  13. H. K. Janssen,Z. Phys. B 42:151 (1981).

    Google Scholar 

  14. H. K. Janssen,Z. Phys. B 58:311 (1985).

    Google Scholar 

  15. H. K. Janssen and B. Schmittmann,Z. Phys. B 64:503 (1986).

    Google Scholar 

  16. P. Grassberger,Z. Phys. B 47:365 (1982).

    Google Scholar 

  17. G. Grinstein, Z.-W. Lai, and D. A. Browne,Phys. Rev. A 40:4820 (1989).

    Google Scholar 

  18. R. C. Brower, M. A. Furman, and M. Moshe,Phys. Lett. B 76:213 (1978).

    Google Scholar 

  19. R. Dickman and M. Burschka,Phys. Lett. A 127:132 (1988).

    Google Scholar 

  20. R. Dickman,J. Stat. Phys. 55:997 (1989).

    Google Scholar 

  21. D. Poland,Physica A 173:363 (1991).

    Google Scholar 

  22. T. M. Liggett,Interacting Particle Systems (Springer-Verlag, New York, 1985); R. Durrett,Lecture Notes on Particle Systems and Percolation (Wadsworth, Pacific Grove, California, 1988).

    Google Scholar 

  23. T. E. Harris,Ann. Prob. 2:969 (1974).

    Google Scholar 

  24. F. Schlögl,Z. Phys. B 253:147 (1972).

    Google Scholar 

  25. J. L. Cardy and R. L. Sugar,J. Phys. A 13:L423 (1980).

    Google Scholar 

  26. R. J. Baxter and A. J. Guttmann,J. Phys. A 21:3193 (1988).

    Google Scholar 

  27. R. Dickman and I. Jensen,Phys. Rev. Lett. 67:2391 (1991).

    Google Scholar 

  28. C. Bezuidenhout and G. Grimmett,Ann. Prob. 18:1462 (1990).

    Google Scholar 

  29. I. Jensen,Phys. Rev. A 45:R563 (1992); I. Jensen,Phys. Rev. A 46:7393 (1992).

    Google Scholar 

  30. M. Doi,J. Phys. A 9:1465, 1479 (1976).

    Google Scholar 

  31. P. Grassberger and M. Scheunert,Fortschr. Phys. 28:547 (1980).

    Google Scholar 

  32. L. Peliti,J. Phys. (Paris)46:1469 (1985).

    Google Scholar 

  33. A. J. Guttmann, inPhase Transitions and Critical Phenomena, Vol. 13, C. Domb and J. Lebowitz, eds. (Academic Press, New York, 1989).

    Google Scholar 

  34. J. W. Essam, A. J. Guttmann, and K. De Bell,J. Phys. A 21:3815 (1988).

    Google Scholar 

  35. D. ben-Avraham, R. Bidaux, and L. S. Schulman,Phys. Rev. A 43:7093 (1991).

    Google Scholar 

  36. J. Adler, M. Moshe, and V. Privman, inPercolation Structures and Processes (Annals of the Israel Physical Society, Vol. 5), G. Deutsher, R. Zallen, and J. Adler, eds. (Hilger, Bristol, 1983).

    Google Scholar 

  37. R. Dickman, J.-S. Wang, and I. Jensen,J. Chem. Phys. 94:8252 (1991).

    Google Scholar 

  38. G. A. Baker, Jr.,Essentials of Padé Approximants (Academic Press, New York, 1975).

    Google Scholar 

  39. G. A. Baker, Jr.,Quantitative Theory of Critical Phenomena (Academic Press, New York, 1990), Chapters 13–18.

    Google Scholar 

  40. P. J. Flory,J. Am. Chem. Soc. 61:1518 (1939).

    Google Scholar 

  41. Y. Fan and J. K. Percus,Phys. Rev. Lett. 67:1677 (1991).

    Google Scholar 

  42. A. Baram and D. Kutasov,J. Phys. A 22:L251 (1989).

    Google Scholar 

  43. R. Dickman and T. Tomé,Phys. Rev. A 44:4833 (1991).

    Google Scholar 

  44. W. Kinzel and J. Yeomans,J. Phys. A 14:L163 (1981).

    Google Scholar 

  45. W. Kinzel,Z. Phys. B 58:229 (1985).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, Herbert H. Lehman College, City University of New York, 10468, Bronx, New York

    Iwan Jensen & Ronald Dickman

  2. Institute of Physics, University of Aarhus, DK-8000, Aarhus C, Denmark

    Iwan Jensen

Authors
  1. Iwan Jensen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ronald Dickman
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jensen, I., Dickman, R. Time-dependent perturbation theory for nonequilibrium lattice models. J Stat Phys 71, 89–127 (1993). https://doi.org/10.1007/BF01048090

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01048090

Key words

Search

Navigation