IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v443y2016icp347-354.html
   My bibliography  Save this article

Dimer problem for some three dimensional lattice graphs

Author

Listed:
  • Lin, Fenggen
  • Chen, Ailian
  • Lai, Jiangzhou

Abstract

Dimer problem for three dimensional lattice is an unsolved problem in statistical mechanics and solid-state chemistry. In this paper, we obtain asymptotical expressions of the number of close-packed dimers (perfect matchings) for two types of three dimensional lattice graphs. Let M(G) denote the number of perfect matchings of G. Then log(M(K2×C4×Pn))≈(−1.171⋅n−1.1223+3.146)n, and log(M(K2×P4×Pn))≈(−1.164⋅n−1.196+2.804)n, where log() denotes the natural logarithm. Furthermore, we obtain a sufficient condition under which the lattices with multiple cylindrical and multiple toroidal boundary conditions have the same entropy.

Suggested Citation

  • Lin, Fenggen & Chen, Ailian & Lai, Jiangzhou, 2016. "Dimer problem for some three dimensional lattice graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 347-354.
    • Handle: RePEc:eee:phsmap:v:443:y:2016:i:c:p:347-354
    DOI: 10.1016/j.physa.2015.09.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437115007542
    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.2015.09.027?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. Yan, Weigen & Yeh, Yeong-Nan & Zhang, Fuji, 2008. "Dimer problem on the cylinder and torus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6069-6078.
    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. Li, Shuli & Yan, Weigen, 2016. "Dimers on the 33.42 lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 251-257.
    2. Marčetić, Dušanka & Elezović-Hadžić, Sunčica & Živić, Ivan, 2020. "Statistics of close-packed dimers on fractal lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    3. Feng, Xing & Zhang, Lianzhu & Zhang, Mingzu, 2018. "Enumeration of perfect matchings of lattice graphs by Pfaffians," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 412-420.
    4. Li, Wei & Zhang, Heping, 2012. "Dimer statistics of honeycomb lattices on Klein bottle, Möbius strip and cylinder," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3833-3848.
    5. Lu, Fuliang & Zhang, Lianzhu & Lin, Fenggen, 2011. "Dimer statistics on the Klein bottle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2315-2324.
    6. Yan, Weigen & Zhang, Zuhe, 2009. "Asymptotic energy of lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1463-1471.

    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:443:y:2016:i:c:p:347-354. 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.