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The complete system of algebraic invariants for the sixteen-vertex model

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  • Gaaff, A.
  • Hijmans, J.

Abstract

The construction of a complete system of basic invariants for the sixteen-vertex model on an M x N lattice as described in part I is repeated by means of an alternative method based on the theory of algebraic invariants. We use a generalization of a theorem by Cayley and Sylvester to determine the characteristics of the covariants belonging to the basic system. In this way we arrive at the same set of 21 invariants that was found in part I. The present method offers the possibility of a generalization to the three-dimensional 64-vertex model and the vertex model on a triangular lattice.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:83:y:1976:i:2:p:317-338
    DOI: 10.1016/0378-4371(76)90039-X
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    References listed on IDEAS

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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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