Scaling of the atmosphere of self-avoiding walks

Details Scaling of the atmosphere of self-avoiding walks Scaling of the atmosphere of self-avoiding walks

2008-06-06

arxiv.org/abs/0806.1250v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1088/1751-8113/41/37/375004

The number of free sites next to the end of a self-avoiding walk is known as the atmosphere. The average atmosphere can be related to the number of configurations. Here we study the distribution of atmospheres as a function of length and how the number of walks of fixed atmosphere scale. Certain bounds on these numbers can be proved. We use Monte Carlo estimates to verify our conjectures. Of particular interest are walks that have zero atmosphere, which are known as trapped. We demonstrate that these walks scale in the same way as the full set of self-avoiding walks, barring an overall constant factor.

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