IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v682y2026ics0378437125008428.html

Distribution functions in site percolation and magnetic frustration

Author

Listed:
  • Lebrecht D-P, W.

Abstract

An alternative model is presented to study site percolation and frustration when monomers and dimers are deposited on square and triangular lattices. To this end, 77 square cell configurations and 82 triangular cell configurations are considered. The configurations allow the determination of a distribution function whose maximum corresponds to the site percolation threshold using a semi-analytical technique. Next, frustration is induced in the cells through ±J interactions of nearest neighbors, using the formal definition of frustrated plaquettes. New distributions are established to determine the level of frustration of the configurations, which leads to the identification of similarities with spin glass properties. In this sense, the work proposes a semi-analytical extension of the site percolation model that incorporates magnetic frustration and establishes a link with spin-glass-like systems.

Suggested Citation

  • Lebrecht D-P, W., 2026. "Distribution functions in site percolation and magnetic frustration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 682(C).
    • Handle: RePEc:eee:phsmap:v:682:y:2026:i:c:s0378437125008428
    DOI: 10.1016/j.physa.2025.131190
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437125008428
    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.2025.131190?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Pezzella, Umberto & Coniglio, Antonio, 1997. "Spin glasses and frustrated percolation: a renormalization group approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 237(3), pages 353-362.
    2. R. Hackl & I. Morgenstern, 1996. "A Correlation Between Percolation Model And Ising Model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 609-612.
    3. V. Cornette & A. Ramirez-Pastor & F. Nieto, 2003. "Percolation of polyatomic species on a square lattice," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 36(3), pages 391-399, December.
    4. Coniglio, Antonio, 1999. "Frustrated percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 379-389.
    5. Lebrecht, W. & Centres, P.M. & Ramirez-Pastor, A.J., 2019. "Analytical approximation of the site percolation thresholds for monomers and dimers on two-dimensional lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 133-143.
    6. A. Rosowsky, 2000. "An analytical method to compute an approximate value of the site percolation threshold P c," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 15(1), pages 77-86, May.
    7. V. A. Cherkasova & Y. Y. Tarasevich & N. I. Lebovka & N. V. Vygornitskii, 2010. "Percolation of aligned dimers on a square lattice," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 74(2), pages 205-209, March.
    8. M. Dolz & F. Nieto & A. J. Ramirez-Pastor, 2005. "Dimer site-bond percolation on a square lattice," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 43(3), pages 363-368, February.
    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. Lebrecht, W., 2025. "Empirical equation for determining critical frontiers of mixed site-bond percolation in Archimedean lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 661(C).
    2. D. Dujak & A. Karač & Lj. Budinski-Petković & Z. M. Jakšić & S. B. Vrhovac, 2022. "Percolation and jamming properties in particle shape-controlled seeded growth model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(9), pages 1-16, September.
    3. Tarasevich, Yuri Yu. & Laptev, Valeri V. & Goltseva, Valeria A. & Lebovka, Nikolai I., 2017. "Influence of defects on the effective electrical conductivity of a monolayer produced by random sequential adsorption of linear k-mers onto a square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 195-203.
    4. Lin, Jianjun & Chen, Huisu & Liu, Lin & Zhang, Rongling, 2020. "Impact of particle size ratio on the percolation thresholds of 2D bidisperse granular systems composed of overlapping superellipses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    5. Huang, Xudong & Yang, Dong & Kang, Zhiqin, 2021. "Impact of pore distribution characteristics on percolation threshold based on site percolation theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).
    6. Javaheri, Parishad & Sadeghnejad, Saeid & Ghanbarian, Behzad & Schäfer, Thorsten, 2025. "Analysis of inter-well connectivity in underground geological reservoirs via percolation theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 678(C).
    7. Šćepanović, J.R. & Karač, A. & Jakšić, Z.M. & Budinski-Petković, Lj. & Vrhovac, S.B., 2019. "Group chase and escape in the presence of obstacles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 450-465.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:682:y:2026:i:c:s0378437125008428. 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.