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The chiral potts model and its associated link invariant

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Abstract

A new link invariant is derived using the exactly solvable chiral Potts model and a generalized Gaussian summation identity. Starting from a general formulation of link invariants using edge-interaction spin models, we establish the uniqueness of the invariant for self-dual models. We next apply the formulation to the self-dual chiral Potts model, and obtain a link invariant in the form of a lattice sum defined by a matrix associated with the link diagram. A generalized Gaussian summation identity is then used to carry out this lattice sum, enabling us to cast the invariant into a tractable form. The resulting expression for the link invariant is characterized by roots of unity and does not appear to belong to the usual quantum group family of invariants. A table of invariants for links with up to eight crossings is given.

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Wu, F.Y., Pant, P. & King, C. The chiral potts model and its associated link invariant. J Stat Phys 78, 1253–1276 (1995). https://doi.org/10.1007/BF02180131

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Key Words

  • Link invariants
  • chiral Potts model
  • generalized Gaussian summation identity