On the criticality of random knots at the θ temperature : A preliminary report(Knots and soft-matter physics: Topology of polymers and related topics in physics, mathematics and biology)

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  • On the criticality of random knots at the θ temperature: a preliminary report
  • On the criticality of random knots at the th temperature a preliminary report

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Abstract

Through simulation using knot invariants we suggest that random polygons under a topological constraint (i.e. random knots) should have novel critical behavior. We recall that the mean-square radius of gyration of random knots with N nodes increases with respect to N almost as that of the self-avoiding polygons, as was pointed out by many authors previously. We find that the two-point correlation function is well approximated by a function close to the Gaussian one. Furthermore, our preliminary data analysis for N=1000 also suggest the simialr result. However, the Gaussian behavior is not consistent with the criticality of the self-avoiding walk. We thus suggest that random knots should have nontrivial and new crtical behavior.

Journal

  • 物性研究

    物性研究 92 (1), 131-134, 2009-04-20

    物性研究刊行会

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