A new Q-matrix in the Eight-Vertex Model

Abstract

We construct a $Q$-matrix for the eight-vertex model at roots of unity for crossing parameter $\eta =2mK/L$ 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 $t\ne 0$, 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.

10 pages section on quasiperiodicity added, typo corrected, published version

References in corpus (1)

• Analytic theory of the eight-vertex model

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