A rapidity-independent parameter in the star-triangle relation

Details A rapidity-independent parameter in the star-triangle relation A rapidity-independent parameter in the star-triangle relation

2001-08-23

arxiv.org/abs/cond-mat/0108363v1

Physics

Condensed Matter

Statistical Mechanics

18 pages

Scientific paper

The normalization factor in the star-triangle relation can be evaluated in a simple form by taking determinants. If we combine this with the rotation symmetries, then we can show that a certain simple quantity $I$ has to be independent of the rapidities. In this sense it is an invariant. We evaluate it for several particular models and find it is one for self-dual models, and is related to the modulus $k$ (or $k'$) for the Ising, Kashiwara-Miwa and chiral Potts models.

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