Geodesic
Spin models on finite cyclic groups
Journal of Algebraic Combinatorics, Tome 3 (1994) no. 3, pp. 243-259.

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Summary: The concept of spin model is due to V. F. R. Jones. The concept of nonsymmetric spin model, which generalizes that of the original (symmetric) spin model, is defined naturally. In this paper, we first determine the diagonal matrices $T$ satisfying the modular invariance or the quasi modular invariance property, i.e., $( PT) ^{3} = \"O{ mP ^{2} }$ (PT)^$3 = \sqrt $mP^2 or $( PT) ^{3} = m ^{\frac32} I$ (PT)^3 = m^frac32 I (respectively), for the character table $P$ of the group association scheme of a cyclic group $G$ of order $m$. Then we show that a (symmetric or nonsymmetric) spin model on $G$ is constructed from each of the matrices $T$ satisfying the modular or quasi modular invariance property.
Keywords: spin model, association scheme, cyclic group, modular invariance property, link invariant 
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     title = {Spin models on finite cyclic groups},
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Bannai, Eiichi; Bannai, Etsuko. Spin models on finite cyclic groups. Journal of Algebraic Combinatorics, Tome 3 (1994) no. 3, pp. 243-259. http://geodesic.mathdoc.fr/item/JAC_1994__3_3_a4/