Twisted Extensions of Spin Models
K. Nomura
DOI: 10.1023/A:1022485615041
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 4 n 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.
Pages: 173–182
Keywords: spin model; star-triangle relation
Full Text: PDF
References
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14. K. Nomura, "Spin models constructed from Hadamard matrices," /. Combin. Theory Ser. A, to appear.
15. D. Rolfsen, "PL link isotopy, essential knotting and quotients of polynomials," Can. Math. Bull., to appear.
2. P. de la Harpe, "Spin models for link polynomials, strongly regular graphs and Jaeger's Higman-Sims model," Pac. J. Math., to appear.
3. F. Jaeger, "Strongly regular graphs and spin models for the Kauffman polynomial," Geom. Dedicate 44 (1992), 23-52.
4. F. Jaeger, "On spin models, triply regular association schemes, and duality," J. Alg. Comb. 4 (199), 103-144.
5. F. Jaeger, "On Nomura's Hadamard spin models and the Jones polynomial, in preparation.
6. G. T. Jin and D. Rolfsen, "Some remarks on rotors in link theory," Can. Math. Bull, to appear.
7. V. F. R. Jones, "A polynomial invariant for knots via von Neumann algebras," Bull. Am. Math. Stic. 12 (1985), 103-111.
8. V. F. R. Jones, "Hecke algebra representations of braid groups and link polynomials," Ann. a/Math. 126 (1987),335-388.
9. V. F. R. Jones, "On knot invariants related to some statistical mechanical models," Pac. J. Math. 137 (1989), 311-336.
10. V. F. R. Jones, "On a certain value of the Kauffman polynomial," Commun. Math. Phys. 125 (1989), 459-467.
11. V. F. R. Jones, "Commuting transfer matrices and link polynomials," International]. Math. 3(1992), 205-212.
12. V. F. R. Jones, Private communication.
13. K. Kawagoe, A. Munemasa, and Y. Watatani, "Generalized spin models," submitted.
14. K. Nomura, "Spin models constructed from Hadamard matrices," /. Combin. Theory Ser. A, to appear.
15. D. Rolfsen, "PL link isotopy, essential knotting and quotients of polynomials," Can. Math. Bull., to appear.