IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v296y2001i1p183-233.html
   My bibliography  Save this article

Exact Potts model partition functions on strips of the honeycomb lattice

Author

Listed:
  • Chang, Shu-Chiuan
  • Shrock, Robert

Abstract

We present exact calculations of the partition function of the q-state Potts model on (i) open, (ii) cyclic, and (iii) Möbius strips of the honeycomb (brick) lattice of width Ly=2 and arbitrarily great length. In the infinite-length limit the thermodynamic properties are discussed. The continuous locus of singularities of the free energy is determined in the q plane for fixed temperature and in the complex temperature plane for fixed q values. We also give exact calculations of the zero-temperature partition function (chromatic polynomial) and W(q), the exponent of the ground-state entropy, for the Potts antiferromagnet for honeycomb strips of type (iv) Ly=3, cyclic, (v) Ly=3, Möbius, (vi) Ly=4, cylindrical, and (vii) Ly=4, open. In the infinite-length limit we calculate W(q) and determine the continuous locus of points where it is nonanalytic. We show that our exact calculation of the entropy for the Ly=4 strip with cylindrical boundary conditions provides an extremely accurate approximation, to a few parts in 105 for moderate q values, to the entropy for the full 2D honeycomb lattice (where the latter is determined by Monte Carlo measurements since no exact analytic form is known).

Suggested Citation

  • Chang, Shu-Chiuan & Shrock, Robert, 2001. "Exact Potts model partition functions on strips of the honeycomb lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(1), pages 183-233.
    • Handle: RePEc:eee:phsmap:v:296:y:2001:i:1:p:183-233
    DOI: 10.1016/S0378-4371(01)00143-1
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437101001431
    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/S0378-4371(01)00143-1?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.

    Citations

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


    Cited by:

    1. Gong, Helin & Jin, Xian’an, 2017. "A general method for computing Tutte polynomials of self-similar graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 117-129.
    2. Gong, Helin & Jin, Xian’an, 2014. "Potts model partition functions on two families of fractal lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 143-153.
    3. Chang, Shu-Chiuan & Shrock, Robert, 2020. "Asymptotic behavior of acyclic and cyclic orientations of directed lattice graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).

    More about this item

    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:296:y:2001:i:1:p:183-233. 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.

    We have no bibliographic 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.

    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.