### 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 language | English (US) |
---|---|

Article number | 023 |

Pages (from-to) | 4659-4672 |

Number of pages | 14 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 25 |

Issue number | 17 |

DOIs | |

State | Published - 1992 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and General*,

*25*(17), 4659-4672. [023]. https://doi.org/10.1088/0305-4470/25/17/023

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

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 25, no. 17, 023, pp. 4659-4672. https://doi.org/10.1088/0305-4470/25/17/023

}

TY - JOUR

T1 - Algebraic invariants of knots and disordered Potts model

AU - Grosberg, A.

AU - Nechaev, S.

PY - 1992

Y1 - 1992

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0000122530&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000122530&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/25/17/023

DO - 10.1088/0305-4470/25/17/023

M3 - Article

AN - SCOPUS:0000122530

VL - 25

SP - 4659

EP - 4672

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 17

M1 - 023

ER -