Abstract
We present two kinds of integral solutions to the quantum Knizhnik–Zamolodchikov equations for the 2n-point correlation functions of the Heisenberg XYZ antiferromagnet. Our first integral solution can be obtained from those for the cyclic SOS model by using the vertex–face correspondence. By the construction, the sum with respect to the local height variables k0, k1, ..., k2n of the cyclic SOS model remains other than the n-fold integral in the first solution. In order to perform these summations, we improve this to find the second integral solution of (r + 1)n-fold integral for r ∊ >1, where r is a parameter of the XYZ model. Furthermore, we discuss the relations among our formula, Lashkevich–Pugai's formula and that of Shiraishi.
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