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Journal of Statistical Physics

, Volume 78, Issue 5–6, pp 1253–1276 | Cite as

The chiral potts model and its associated link invariant

  • F. Y. Wu
  • P. Pant
  • C. King
Articles

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.

Key Words

Link invariants chiral Potts model generalized Gaussian summation identity 

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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • F. Y. Wu
    • 1
  • P. Pant
    • 1
  • C. King
    • 2
  1. 1.Department of PhysicsNortheastern UniversityBoston
  2. 2.Department of MathematicsNortheastern UniversityBoston

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