Equilibrium winding angle of a polymer around a bar

Details Equilibrium winding angle of a polymer around a bar Equilibrium winding angle of a polymer around a bar

2011-10-21

arxiv.org/abs/1110.4782v2

J. Stat. Mech. (2011) P10020

Physics

Condensed Matter

Statistical Mechanics

18 pages, 12 figures, 1 table

Scientific paper

10.1088/1742-5468/2011/10/P10020

The winding angle probability distribution of a planar self-avoiding walk has been known exactly since a long time: it has a gaussian shape with a variance growing as $<\theta^2>\sim \ln L$. For the three-dimensional case of a walk winding around a bar, the same scaling is suggested, based on a first-order epsilon-expansion. We tested this three-dimensional case by means of Monte Carlo simulations up to length $L\approx25\,000$ and using exact enumeration data for sizes $L\le20$. We find that the variance of the winding angle scales as $<\theta^2>\sim (\ln L)^{2\alpha}$, with $\alpha=0.75(1)$. The ratio $\gamma = <\theta^4>/<\theta^2>^2=3.74(5)$ is incompatible with the gaussian value $\gamma =3$, but consistent with the observation that the tail of the probability distribution function $p(\theta)$ is found to decrease slower than a gaussian function. These findings are at odds with the existing first-order $\epsilon$-expansion results.

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