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arXiv · 1506.00296

Compressed self-avoiding walks, bridges and polygons

Nicholas R. Beaton·Anthony J. Guttmann·Iwan Jensen·Gregory F. Lawler
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Abstract

We study various self-avoiding walks (SAWs) which are constrained to lie in the upper half-plane and are subjected to a compressive force. This force is applied to the vertex or vertices of the walk located at the maximum distance above the boundary of the half-space. In the case of bridges, this is the unique end-point. In the case of SAWs or self-avoiding polygons, this corresponds to all vertices of maximal height. We first use the conjectured relation with the Schramm-Loewner evolution to predict the form of the partition function including the values of the exponents, and then we use series analysis to test these predictions.

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Nicholas R. Beaton, Anthony J. Guttmann, Iwan Jensen, Gregory F. Lawler. 2015-05-31. Compressed self-avoiding walks, bridges and polygons. https://doi.org/10.1088/1751-8113/48/45/454001

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