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

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  • 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
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    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.
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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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.

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