Spin Models Constructed from Hadamard Matrices

Abstract New spin models are constructed from Hadamard matrices. Spin models were defined by V. F. R. Jones (1989, Pacific J. Math. 137 , 311–336). F. Jaeger (1992, Geom. Dedicata 44 , 23–52) gives a method for obtaining spin models from association schemes and he studies spin models on strongly regular graphs. E. Bannai and E. Bannai (Spin models on finite cyclic groups, preprint) construct spin models from cyclic groups. In this paper, we construct spin models from a certain class of distance-regular graphs, associated to Hadamard matrices. We obtain a spin model with loop variables D = 4√ m from an arbitrary Hadamard matrix of order 4 m .