Skip to main content
SpringerLink
Log in

Structure of two-dimensional sandpile. I. Height probabilities

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

Abstract

The height probabilities of the two-dimensional Abelian sandpile model are the fractionial numbers of lattice sites having heights 1, 2, 3, 4. A combinatorial method for evaluation of these quantities is proposed. The method is based on mapping the set of allowed sandpile configurations onto the set of spanning trees covering a given lattice. Exact analytical expressions for all probabilities are obtained.

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.

Similar content being viewed by others

Refrences

  1. P. Bak, C Tang, and K. Wiesenfeld,Phys. Rev. Lett.,59:381 (1987);Phys. Rev. A 38:364 (1988).

    Google Scholar 

  2. J. M. Carlson and J. S. Langer,Phys. Res. Lett.,62:2632 (1989); K. Chen. P. Bak. and S. P. Obukhov,Phys. Rev. A 43:625 (1990).

    Google Scholar 

  3. I. McHardy and B. Czerny,Nature 325:696 (1987).

    Google Scholar 

  4. P. Dutta and P. M. Horn,Rev. Mod. Phys. 53:497 (1981).

    Google Scholar 

  5. H. Takayasu,Phys. Rev. Lett. 63:2563 (1989).

    Google Scholar 

  6. X. Che and H. Suhl,Phys. Rev. Lett. 64:1670 (1990).

    Google Scholar 

  7. E. H. Miranda and H. J. Herrmann,Physica A 175:379 (1991).

    Google Scholar 

  8. D. Dhar,Phys. Rev. Lett. 64:1613 (1990).

    Google Scholar 

  9. V. B. Priezzhev, Preprint DIAS-STP-92-10; submitted toProceedings of 13th General Conference of EPS, Regensburg, March 1993.

  10. Y. C. Zhang,Phys. Rev. Lett. 63:470 (1989).

    Google Scholar 

  11. A. Erzan and S. Shina, Preprint ICTP, Trieste (1990).

  12. S. S. Manna,J. Stat. Phys. 59:509 (1990).

    Google Scholar 

  13. P. Grassberger and S. S. Manna,J. Phys. (Paris)51:1077 (1990).

    Google Scholar 

  14. S.N. Majumdar and D. Dhar,J. Phys. A 24:L357 (1991).

    Google Scholar 

  15. S.N. Majumdar and D. Dhar,Physica A 185:129 (1992).

    Google Scholar 

  16. F. Harary and E. H. Palmer,Graphical Enumeration (Academic Press, New York, 1973).

    Google Scholar 

  17. F. Spitzer,Principles of Random Walk (Van Nostrand, 1964).

  18. P. W. Kasteleyn, InGraph Theory and Theoretical Physics, F. Harary, ed. (Academic Press, London, 1967), pp. 44–110.

    Google Scholar 

  19. V. B. Priezzhev,Sov. Phys. Usp. 28:1125 (1985).

    Google Scholar 

  20. C. Pan and F. Y. Wu,Phys. Rev. B 2:723 (1970).

    Google Scholar 

  21. R. J. Baxter,Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, Russia

    V. B. Priezzhev

Authors
  1. V. B. Priezzhev
    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

Priezzhev, V.B. Structure of two-dimensional sandpile. I. Height probabilities. J Stat Phys 74, 955–979 (1994). https://doi.org/10.1007/BF02188212

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02188212

Key Words

Search

Navigation