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Symmetry relations in the sixteen-vertex model

Author

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  • Gaaff, A.
  • Hijmans, J.

Abstract

We explore the consequences of the existence of a group of linear symmetry transformations for the sixteen-vertex model. An arbitrary sixteen-vertex model is shown tobe equivalent to a standard model, described in terms of ten parameters having an invariant significance. The general eight-vertex model is obtained when four of the invariant parameters vanish. Two further subciasses of the sixteen-vertex model are found to be equivalent to the eight-vertex model. The invariant conditions leading to the solved cases (i.e the general six-vertex, the free-fermion and the symmetric eight-vertex models) are given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:80:y:1975:i:2:p:149-171
    DOI: 10.1016/0378-4371(75)90164-8
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    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 442-464.
    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 425-441.
    7. 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.
    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. 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.
    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. 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.
    12. 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.
    13. 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.
    14. 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.

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