Abstract
The probability distribution of the winding angle theta of a planar self-avoiding walk has been known exactly for a long time: it has a Gaussian shape with a variance growing as similar to 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 approximate to 25 000 and using exact enumeration data for sizes L (ln L)(2 alpha), with alpha = 0.75(1). The ratio gamma = /(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 more slowly than a Gaussian function. These findings are at odds with the existing first-order epsilon-expansion results.
Original language | English |
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Article number | 10020 |
Number of pages | 16 |
Journal | Journal of Statistical Mechanics: Theory and Experiment |
DOIs | |
Publication status | Published - Oct 2011 |
Keywords
- classical Monte Carlo simulations
- finite-size scaling
- polymer elasticity
- SELF-AVOIDING WALKS
- STATISTICAL-MECHANICS
- DNA DENATURATION
- DISTRIBUTIONS
- MODEL