IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v580y2021ics0378437121003976.html
   My bibliography  Save this article

Critical exponents and universal excess cluster number of percolation in four and five dimensions

Author

Listed:
  • Zhang, Zhongjin
  • Hou, Pengcheng
  • Fang, Sheng
  • Hu, Hao
  • Deng, Youjin

Abstract

We study critical bond percolation on periodic four-dimensional (4D) and five-dimensional (5D) hypercubes by Monte Carlo simulations. By classifying the occupied bonds into branches, junctions and non-bridges, we construct the whole, the leaf-free and the bridge-free clusters using the breadth-first search algorithm. From the geometric properties of these clusters, we determine a set of four critical exponents, including the thermal exponent yt≡1∕ν, the fractal dimension df, the backbone exponent dB and the shortest-path exponent dmin. We also obtain an estimate of the excess cluster number b which is a universal quantity related to the finite-size scaling of the total number of clusters. The results are yt=1.461(5), df=3.0446(7), dB=1.9844(11), dmin=1.6042(5), b=0.62(1) for 4D; and yt=1.743(10), df=3.5260(14), dB=2.0226(27), dmin=1.8137(16), b=0.62(2) for 5D. The values of the critical exponents are compatible with or improving over the existing estimates, and those of the excess cluster number b have not been reported before. Together with the existing values in other spatial dimensions d, the d-dependent behavior of the critical exponents is obtained, and a local maximum of dB is observed near d≈5. It is suggested that, as expected, critical percolation clusters become more and more dendritic as d increases.

Suggested Citation

  • Zhang, Zhongjin & Hou, Pengcheng & Fang, Sheng & Hu, Hao & Deng, Youjin, 2021. "Critical exponents and universal excess cluster number of percolation in four and five dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    • Handle: RePEc:eee:phsmap:v:580:y:2021:i:c:s0378437121003976
    DOI: 10.1016/j.physa.2021.126124
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437121003976
    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
    File URL: https://libkey.io/10.1016/j.physa.2021.126124?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Daniel Tiggemann, 2001. "Simulation Of Percolation On Massively-Parallel Computers," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(06), pages 871-878.
    2. C. Moukarzel, 1998. "A Fast Algorithm for Backbones," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 9(06), pages 887-895.
    3. Ziff, Robert M & Lorenz, Christian D & Kleban, Peter, 1999. "Shape-dependent universality in percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 17-26.
    4. Grassberger, Peter, 1999. "Conductivity exponent and backbone dimension in 2-d percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 262(3), pages 251-263.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    2. Stanley, H.Eugene & Andrade, José S. & Havlin, Shlomo & Makse, Hernán A. & Suki, Béla, 1999. "Percolation phenomena: a broad-brush introduction with some recent applications to porous media, liquid water, and city growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 5-16.
    3. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.
    4. He, Zhenfang & Hu, Hao, 2021. "Size distributions of the largest hole in the largest percolation cluster and backbone," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).
    5. Gross, Bnaya & Bonamassa, Ivan & Havlin, Shlomo, 2021. "Interdependent transport via percolation backbones in spatial networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    6. Stanley, H.Eugene & Andrade, José S, 2001. "Physics of the cigarette filter: fluid flow through structures with randomly-placed obstacles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 17-30.

    Corrections

    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:580:y:2021:i:c:s0378437121003976. See general information about how to correct material in RePEc.

    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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.