Spin models constructed from Hadamard matrices

TL;DR

This paper introduces a method to construct spin models of any even index from Hadamard matrices, including new models of indices that are powers of two, expanding the toolkit for link invariant studies.

Contribution

It provides a novel construction technique for spin models of arbitrary even index using Hadamard matrices, including new models for indices that are powers of two.

Findings

Constructed spin models of arbitrary even index from Hadamard matrices.

Identified new spin models with indices that are powers of two.

Extended the class of known spin models for link invariants.

Abstract

A spin model (for link invariants) is a square matrix $W$ which satisfies certain axioms. For a spin model $W$, it is known that $W^TW^{-1}$ is a permutation matrix, and its order is called the index of $W$. F. Jaeger and K. 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.