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A new Q-matrix in the Eight-Vertex Model

Klaus Fabricius
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Abstract

We construct a $Q$-matrix for the eight-vertex model at roots of unity for crossing parameter $η=2mK/L$ with odd $L$, a case for which the existing constructions do not work. The new $Q$-matrix $\Q$ depends as usual on the spectral parameter and also on a free parameter $t$. For $t=0$ $\Q$ has the standard properties. For $t\neq 0$, however, it does not commute with the operator $S$ and not with itself for different values of the spectral parameter. We show that the six-vertex limit of $\Q(v,t=iK'/2)$ exists.

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Klaus Fabricius. 2007-09-10. A new Q-matrix in the Eight-Vertex Model. https://doi.org/10.1088/1751-8113%2F40%2F15%2F002

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