Abstract
A spin model is one of the statistical mechanical models which were introduced by V.F.R. Jones to construct invariants of links. In this paper, we give a new construction of spin models of size 4n from a given spin model of size n. The process is similar to taking tensor product with a spin model of size four, but we add some sign exchange. This construction also gives symmetric four-weight spin models of the type introduced by E. Bannai and E. Bannai.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Bannai and E. Bannai, “Four-weight spin models,” Pac. J. Math., to appear.
P. de la Harpe, “Spin models for link polynomials, strongly regular graphs and Jaeger's Higman-Sims model,” Pac. J. Math., to appear.
F. Jaeger, “Strongly regular graphs and spin models for the Kauffman polynomial,” Geom. Dedicata 44 (1992), 23–52.
F. Jaeger, “On spin models, triply regular association schemes, and duality,” J. Alg. Comb. 4 (199), 103–144.
F. Jaeger, “On Nomura's Hadamard spin models and the Jones polynomial, in preparation.
G. T. Jin and D. Rolfsen, “Some remarks on rotors in link theory,” Can. Math. Bull., to appear.
V.F.R. Jones, “A polynomial invariant for knots via von Neumann algebras,” Bull. Am. Math. Soc. 12 (1985), 103–111.
V.F R. Jones, “Hecke algebra representations of braid groups and link polynomials,” Ann. of Math. 126 (1987), 335–388.
V.F.R. Jones, “On knot invariants related to some statistical mechanical models,” Pac. J. Math. 137 (1989), 311–336.
V.F.R. Jones, “On a certain value of the Kauffman polynomial,” Commun. Math. Phys. 125 (1989), 459–467.
V.F.R. Jones, “Commuting transfer matrices and link polynomials,” International J. Math. 3(1992), 205–212.
V.F.R. Jones, Private communication.
K. Kawagoe, A. Munemasa, and Y. Watatani, “Generalized spin models,” submitted.
K. Nomura, “Spin models constructed from Hadamard matrices,” J. Combin. Theory Ser. A, to appear.
D. Rolfsen, “PL link isotopy, essential knotting and quotients of polynomials,” Can. Math. Bull., to appear.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nomura, K. Twisted Extensions of Spin Models. Journal of Algebraic Combinatorics 4, 173–182 (1995). https://doi.org/10.1023/A:1022485615041
Issue Date:
DOI: https://doi.org/10.1023/A:1022485615041