Algebraic invariants of knots and disordered Potts model

A. Grosberg, S. Nechaev

    Research output: Contribution to journalArticle

    Abstract

    The authors propose the reformulation of the Kauffman bracket invariant of the knot in terms of statistical mechanics of the 2D disordered Potts model. This allows one to put the question of the determination of knot entropy (or of the probability of an arbitrary knot formation) in terms of usual statistical mechanics. To demonstrate the possibilities of their approach they give a constructive estimation for the trivial knot formation probability for a long strongly contracted closed random path confined in a thin slit. They use the mean-field approximation for the free energy of the Potts system at the point of the transition from the paramagnetic phase to the spin-glass one.

    Original languageEnglish (US)
    Article number023
    Pages (from-to)4659-4672
    Number of pages14
    JournalJournal of Physics A: Mathematical and General
    Volume25
    Issue number17
    DOIs
    StatePublished - 1992

    Fingerprint

    Potts model
    Statistical mechanics
    Potts Model
    statistical mechanics
    Knot
    Spin glass
    Invariant
    brackets
    Statistical Mechanics
    spin glass
    Free energy
    slits
    Entropy
    free energy
    Kauffman Bracket
    entropy
    Mean-field Approximation
    Spin Glass
    Reformulation
    approximation

    ASJC Scopus subject areas

    • Mathematical Physics
    • Physics and Astronomy(all)
    • Statistical and Nonlinear Physics

    Cite this

    Algebraic invariants of knots and disordered Potts model. / Grosberg, A.; Nechaev, S.

    In: Journal of Physics A: Mathematical and General, Vol. 25, No. 17, 023, 1992, p. 4659-4672.

    Research output: Contribution to journalArticle

    Grosberg, A. ; Nechaev, S. / Algebraic invariants of knots and disordered Potts model. In: Journal of Physics A: Mathematical and General. 1992 ; Vol. 25, No. 17. pp. 4659-4672.
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