Geodesic
Spin models of index 2 and Hadamard models
Journal of Algebraic Combinatorics, Tome 17 (2003) no. 1, pp. 5-17.

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Summary: A spin model (for link invariants) is a square matrix $W$ with non-zero complex entries which satisfies certain axioms. Recently it was shown that $^{t} WW ^{-1}$ is a permutation matrix (the order of this permutation matrix is called the $ldquo$index $rdquo$ of $W$), and a general form was given for spin models of index 2. Moreover, new spin models, called non-symmetric Hadamard models, were constructed. In the present paper, we classify certain spin models of index 2, including non-symmetric Hadamard models.
Keywords: spin model, association scheme, Hadamard matrix, Potts model 
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Nomura, Kazumasa. Spin models of index 2 and Hadamard models. Journal of Algebraic Combinatorics, Tome 17 (2003) no. 1, pp. 5-17. http://geodesic.mathdoc.fr/item/JAC_2003__17_1_a4/