Spin models constructed from Hadamard matrices

Takuya Ikuta, Akihiro Munemasa

Research output: Contribution to journalArticlepeer-review


A spin model (for link invariants) is a square matrix W which satisfies certain axioms. For a spin model W, it is known that WT W -1 is a permutation matrix, and its order is called the index of W. Jaeger and Nomura found spin models of index 2, by modifying the construction of symmetric spin models from Hadamard matrices. The aim of this paper is to give a construction of spin models of an arbitrary even index from any Hadamard matrix. In particular, we show that our spin models of indices a power of 2 are new.

Original languageEnglish
Pages (from-to)231-248
Number of pages18
JournalJournal of Applied Mathematics and Computing
Issue number1-2
Publication statusPublished - 2012 Oct


  • Association scheme
  • Hadamard matrix
  • Spin model


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