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Jones polynomials and their zeros for a family of links

Author

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  • Jin, Xian'an
  • Zhang, Fuji

Abstract

In this paper, we define a family of links which are similar to but more complex than Pretzel links. We compute the exact expressions of the Jones polynomials for this family of links. Motivated by the connection with the Potts model in statistical mechanics, we investigate accumulation points of zeros of the Jones polynomials for some subfamilies.

Suggested Citation

  • Jin, Xian'an & Zhang, Fuji, 2004. "Jones polynomials and their zeros for a family of links," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 183-196.
    • Handle: RePEc:eee:phsmap:v:333:y:2004:i:c:p:183-196
    DOI: 10.1016/j.physa.2003.10.085
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    References listed on IDEAS

    as
    1. Chang, S.-C. & Shrock, R., 2001. "Zeros of Jones polynomials for families of knots and links," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 196-218.
    2. Jin, Xian'an & Zhang, Fuji, 2003. "Zeros of the Jones polynomials for families of pretzel links," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(3), pages 391-408.
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    Cited by:

    1. Kassenova, T.K. & Tsyba, P.Yu. & Razina, O.V. & Myrzakulov, R., 2022. "Three-partite vertex model and knot invariants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).

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    1. Kassenova, T.K. & Tsyba, P.Yu. & Razina, O.V. & Myrzakulov, R., 2022. "Three-partite vertex model and knot invariants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    2. Jin, Xian'an & Zhang, Fuji, 2003. "Zeros of the Jones polynomials for families of pretzel links," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(3), pages 391-408.

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