IDEAS home Printed from
   My bibliography  Save this article

Stochastic sandpile model on small-world networks: Scaling and crossover


  • Bhaumik, Himangsu
  • Santra, S.B.


A dissipative stochastic sandpile model is constructed on one and two dimensional small-world networks with shortcut density ϕ, ϕ=0 represents a regular lattice whereas ϕ=1 represents a random network. The effect of the transformation of the regular lattice to a small-world network on the critical behaviour of the model as well as the role of dimensionality of the underlying regular lattice are explored studying different geometrical properties of the avalanches as a function of avalanche size s in the small-world regime (2−12≤ϕ≤0.1). For both the dimensions, three regions of s, separated by two crossover sizes s1 and s2 (s1s1 are sparse as they are on network and follow mean-field scaling. Coexistence of different scaling forms in the small-world regime leads to violation of usual finite-size scaling which were valid on the regular lattice as well as on the random network independently. Simultaneous appearance of multiple scaling forms are characterized by developing a coexistence scaling theory. As SWN evolves from regular lattice to random network, a crossover from diffusive to super-diffusive nature of sand transport is observed and scaling forms of such crossover is developed and verified.

Suggested Citation

  • Bhaumik, Himangsu & Santra, S.B., 2018. "Stochastic sandpile model on small-world networks: Scaling and crossover," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 358-370.
  • Handle: RePEc:eee:phsmap:v:511:y:2018:i:c:p:358-370
    DOI: 10.1016/j.physa.2018.08.003

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    As the access to this document is restricted, you may want to search for a different version of it.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:511:y:2018:i:c:p:358-370. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.