IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v182y1992i3p455-466.html
   My bibliography  Save this article

Mapping of the symmetric vertex model onto the Ising model for an arbitrary lattice coordination

Author

Listed:
  • Šamaj, L.
  • Kolesík, M.

Abstract

We investigate the mapping of the two-state symmetric vertex model onto the Ising model in a field for a lattice with general coordination number q. The analysis is based on a combination of decoration and generalized weak-graph transformations. It is shown that the mapping is restricted to the manifold formed by the intersection of q−3 hypersurfaces in the space of symmetric vertex weights. We also derive dual relations among the model parameters and the free energies of the related symmetric vertex and Ising models. The choices of the energies of the vertex configurations for which the mapping can be performed throughout the entire temperature range are briefly discussed.

Suggested Citation

  • Šamaj, L. & Kolesík, M., 1992. "Mapping of the symmetric vertex model onto the Ising model for an arbitrary lattice coordination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 182(3), pages 455-466.
    • Handle: RePEc:eee:phsmap:v:182:y:1992:i:3:p:455-466
    DOI: 10.1016/0378-4371(92)90354-S
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037843719290354S
    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/10.1016/0378-4371(92)90354-S?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. Gaaff, A. & Hijmans, J., 1975. "Symmetry relations in the sixteen-vertex model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 80(2), pages 149-171.
    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. Šamaj, L. & Kolesík, M., 1993. "Self-duality of the O(2) gauge transformation and the phase structure of vertex models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 193(1), pages 157-168.

    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. Kolesik, Miroslav & Suzuki, Masuo, 1995. "Accurate estimates of 3D Ising critical exponents using the coherent-anomaly method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 215(1), pages 138-151.
    2. Gaaff, A. & Hijmans, J., 1976. "The complete system of algebraic invariants for the sixteen-vertex model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 83(2), pages 301-316.
    3. Hijmans, J. & Schram, H.M., 1984. "On the bifurcations occurring in the parameter space of the sixteen vertex model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 125(1), pages 25-57.
    4. Gaaff, A. & Hijmans, J., 1976. "The complete system of algebraic invariants for the sixteen-vertex model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 83(2), pages 317-338.
    5. Colpa, J.H.P., 1984. "On the classification of the homogeneous 16-vertex models on a square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 125(2), pages 425-441.
    6. Colpa, J.H.P., 1984. "On the classification of the homogeneous 16-vertex models on a square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 125(2), pages 442-464.
    7. Kolesík, M. & S̆amaj, L., 1991. "On correlation functions of two-state vertex models on the honeycomb lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 179(1), pages 145-157.
    8. Hijmans, J. & Schram, H.M., 1983. "On the bifurcations occuring in the parameter space of the sixteen vertex model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 121(3), pages 479-512.
    9. Kolesik, Miroslav & Suzuki, Masuo, 1995. "Critical exponents of the 3D antiferromagnetic three-state Potts model using the coherent-anomaly method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 216(4), pages 469-477.
    10. Colpa, J.H.P., 1986. "Diagonalization of the quadratic boson Hamiltonian with zero modes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 134(2), pages 377-416.
    11. Gaaff, A. & Hijmans, J., 1978. "Interpretation of the symmetry group of the homogeneous 16-vertex model in terms of Lorentz similarity transformations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 94(2), pages 192-210.
    12. Gaaff, A. & Hijmans, J., 1979. "Bifurcation analysis of the sixteen-vertex model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 97(2), pages 244-272.
    13. Hijmans, J., 1985. "Simplified bifurcation analysis of the sixteen vertex model, based on the standard representation of equivalence classes of models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 130(1), pages 57-87.

    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:182:y:1992:i:3:p:455-466. 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.