IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v125y1984i2p442-464.html
   My bibliography  Save this article

On the classification of the homogeneous 16-vertex models on a square lattice

Author

Listed:
  • Colpa, J.H.P.

Abstract

In the previous paper we have shown that the classification problem of the homogeneous real 16-vertex models on a square lattice as proposed by Gaaff and Hijmans is closely connected with the similar problem corresponding to the boson Bogoliubov transformation in quantum mechanics. This insight leads us in the present paper to use arguments and examples from papers dealing with the latter problem in a further study of the classification problem of the real 16-vertex models. We also use a somewhat modified concept of “standard (or normal) 16-vertex model” which was introduced by Hijmans and Schram in a similar study concerning the complex 16-vertex models. We show that, rather than the single family found by Hijmans and Schram for the complex variant of the problem, the set of equivalence classes of real 16-vertex models can be divided up into seven families. This strongly suggests the existence of a new type of phase transitions which manifest themselves when the physical system in the 16-parameter space “moves” from one family to another.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:125:y:1984:i:2:p:442-464
    DOI: 10.1016/0378-4371(84)90064-5
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437184900645
    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(84)90064-5?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., 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.
    2. 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)

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.

    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:125:y:1984:i:2:p:442-464. 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.