IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v388y2009i8p1463-1471.html
   My bibliography  Save this article

Asymptotic energy of lattices

Author

Listed:
  • Yan, Weigen
  • Zhang, Zuhe

Abstract

The energy of a simple graph G arising in chemical physics, denoted by E(G), is defined as the sum of the absolute values of eigenvalues of G. As the dimer problem and spanning trees problem in statistical physics, in this paper we propose the energy per vertex problem for lattice systems. In general for a type of lattice in statistical physics, to compute the entropy constant with toroidal, cylindrical, Mobius-band, Klein-bottle, and free boundary conditions are different tasks with different hardness and may have different solutions. We show that the energy per vertex of plane lattices is independent of the toroidal, cylindrical, Mobius-band, Klein-bottle, and free boundary conditions. In particular, the asymptotic formulae of energies of the triangular, 33.42, and hexagonal lattices with toroidal, cylindrical, Mobius-band, Klein-bottle, and free boundary conditions are obtained explicitly.

Suggested Citation

  • Yan, Weigen & Zhang, Zuhe, 2009. "Asymptotic energy of lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1463-1471.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:8:p:1463-1471
    DOI: 10.1016/j.physa.2008.12.058
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437108010820
    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.2008.12.058?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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lei, Hui & Li, Tao & Ma, Yuede & Wang, Hua, 2018. "Analyzing lattice networks through substructures," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 297-314.
    2. Liu, Jia-Bao & Pan, Xiang-Feng, 2015. "Asymptotic incidence energy of lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 193-202.
    3. Liu, Xiaoyun & Yan, Weigen, 2013. "The triangular kagomé lattices revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5615-5621.
    4. Liu, Jia-Bao & Pan, Xiang-Feng, 2015. "A unified approach to the asymptotic topological indices of various lattices," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 62-73.
    5. 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.
    6. Liu, Jia-Bao & Pan, Xiang-Feng & Hu, Fu-Tao & Hu, Feng-Feng, 2015. "Asymptotic Laplacian-energy-like invariant of lattices," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 205-214.

    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. 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.
    5. 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.
    6. 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.

    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:388:y:2009:i:8:p:1463-1471. 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.