In  Yasuo Watatani and Akihiro Munemasa found an example of a nonsymmetric spin model on 3 vertices. In this paper we show that there are no spin models corresponding to nonsymmetric association schemes of class 2 except the ones corresponding to Potts models and the one on three vertices.
We give a short and alternative proof of a theorem of F. Jaeger that except for Potts models attached to the complete graphs, the only spin models associated with symmetric conference graphs with n ≥ 5 vertices are the pentagon and the lattice graph L2(3) with 9 vertices. The proof avoids Jaeger's use of the classification of strongly regular graphs having strongly regular subconstituents due to P. J. Cameron, J. M. Goethals, and J. J. Seidel.
The concept of spin model was defined by V. F. R. Jones. Recently, F. Jaeger discovered that Bose-Mesner algebras of association schemes are natural places to look for spin models. The purpose of this paper is to study connections between (generalized) generalized spin models and (not necessarily symmetric) association schemes. For arbitrary generalized generalized spin models, we can prove somewhat weaker versions of Jaeger's results. However, we prove the corresponding results of Jaeger in full strength for generalized spin models of Jones type.
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