IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v94y1978i2p192-210.html
   My bibliography  Save this article

Interpretation of the symmetry group of the homogeneous 16-vertex model in terms of Lorentz similarity transformations

Author

Listed:
  • Gaaff, A.
  • Hijmans, J.

Abstract

A new analysis is made of the symmetry group of the general homogeneous 16-vertex model on a square lattice, i.e. the group of transformations in the parameter space of the model leaving invariant its partition function. The set of 16 vertex weights is decomposed in such a way that the ensuing matrix P of 16 composite parameters transforms according to the group of Lorentz similarity transformations. Equivalence classes of models can be characterized by a suitably chosen ‘normal’ matrix P(n), depending on 10 parameters, four having the significance of principle values, and the remaining six (two angles and two 3-dimensional unit vectors) determining a Lorentz transformation. The analysis is applied to the general eight-vertex model as well as to its soluble subclasses, the symmetric eight-vertex model, the general six-vertex model and the free fermion model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:94:y:1978:i:2:p:192-210
    DOI: 10.1016/0378-4371(78)90096-1
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437178900961
    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(78)90096-1?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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    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. 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. 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.

    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. 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.
    10. 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.
    11. 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.
    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:94:y:1978:i:2:p:192-210. 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.