WINDING ANGLE DISTRIBUTION OF SELF-AVOIDING WALKS IN TWO DIMENSIONS

Iksoo Chang ()
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Iksoo Chang: Department of Physics, Pusan National University, Pusan 609-735, Korea

International Journal of Modern Physics C (IJMPC), 2000, vol. 11, issue 04, 721-729

Abstract: Winding angle problem of two-dimensional self-avoiding walks (SAWs) on a square lattice is studied intensively by the scanning Monte Carlo simulation at high, theta (Θ), and low-temperatures. The winding angle distributionPN(θ)and the even moments of winding angle$\langle \theta_N^{2k} \rangle$are calculated for lengths of SAWs up toN = 300and compared with the analytical prediction. At the infinite temperature (good solvent regime of linear polymers),PN(θ)is well described by either a Gaussian function or a stretched exponential function which is close to Gaussian, so, it is not incompatible with an analytical prediction that it is a Gaussian functionexp[-θ2/lnN]in terms of a variable$\theta /\sqrt{\ln N}$and that$\langle \theta_N^{2k} \rangle\propto (\ln N)^k$. However, the results for SAWs at Θ and low-temperatures (Θ and bad solvent regime of linear polymers) significantly deviate from this analytical prediction.PN(θ)is then described much better by a stretched exponential functionexp[-|θ|α/ln N]and$\langle \theta_N^{2k} \rangle\propto (\ln N)^{2k/\alpha}$withα = 1.54and 1.51 which is far from being a Gaussian. We provide a consistent numerical evidence that the winding angle distribution for SAWs at the finite temperatures may not be a Gaussian function but a nontrivial distribution, possibly a stretched exponential function.

Keywords: Self-Avoiding Walks; Winding Angle Distribution; Scaling Behavior (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1142/S012918310000064X

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