IDEAS home Printed from
   My bibliography  Save this article

Percolation of dimers on square lattices


  • Lebrecht, W.
  • Valdés, J.F.
  • Vogel, E.E.
  • Nieto, F.
  • Ramirez-Pastor, A.J.


A theoretical approach, based on exact calculations of configurations on finite rectangular cells, is applied to study the percolation of homonuclear dimers on square lattices. An efficient algorithm allows us to calculate the detailed structure of the configuration space for M=Lx×Ly cells, with M varying from 16 to 36. The percolation process has been monitored by following the percolation function, defined as the ratio between the number of percolating configurations and the total number of available configurations for a given cell size and concentration of occupied sites. The percolation threshold has been calculated by means of two complementary methods: one based on well-known renormalization techniques and the other based on determining the inflection point of the percolation function curves. A comparison of the results obtained by these two methods has been performed. The study includes the use of finite-size scaling theory to extrapolate numerical results towards the thermodynamic limit. The effect of jamming due to dimers is also established. Finally, the critical exponents ν, β and γ have been obtained and values compared with numerical results and expected theoretical estimations. The present results show agreement and even improvement (in the case of γ) with respect to some numeric values available in the literature.

Suggested Citation

  • Lebrecht, W. & Valdés, J.F. & Vogel, E.E. & Nieto, F. & Ramirez-Pastor, A.J., 2013. "Percolation of dimers on square lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 149-156.
  • Handle: RePEc:eee:phsmap:v:392:y:2013:i:1:p:149-156 DOI: 10.1016/j.physa.2012.08.014

    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.

    References listed on IDEAS

    1. Isobe, Motoshige & Adachi, Taku & Nagatani, Takashi, 2004. "Experiment and simulation of pedestrian counter flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 638-650.
    2. Zhang, Jun & Song, Weiguo & Xu, Xuan, 2008. "Experiment and multi-grid modeling of evacuation from a classroom," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5901-5909.
    Full references (including those not matched with items on IDEAS)


    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:392:y:2013:i:1:p:149-156. 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.