Baxterization, dynamical systems, and the symmetries of integrability

Details Baxterization, dynamical systems, and the symmetries of integrability Baxterization, dynamical systems, and the symmetries of integrability

1994-03-22

arxiv.org/abs/hep-th/9403130v1

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, Latex file (epsf style). WARNING: Postscript figures are BIG (600kB compressed, 4.3MB uncompressed). If necessary re

Scientific paper

10.1007/3-540-58453-6_2

We resolve the `baxterization' problem with the help of the automorphism group of the Yang-Baxter (resp. star-triangle, tetrahedron, \dots) equations. This infinite group of symmetries is realized as a non-linear (birational) Coxeter group acting on matrices, and exists as such, {\em beyond the narrow context of strict integrability}. It yields among other things an unexpected elliptic parametrization of the non-integrable sixteen-vertex model. It provides us with a class of discrete dynamical systems, and we address some related problems, such as characterizing the complexity of iterations.

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